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ECON 11A Midterm: ECON11A Exan 2017 Winter Solutions

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turquoisegnu128
15 Oct 2018
School
UCSC
Department
Economics
Course
ECON 11A
Professor
All

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Document Summary

Applied optimization and curve sketching: sketch a graph of the function g(x) = Your sketch should clearly indicate: x and y intercepts; critical points and relative extreme values; horizontal asymptotes (i. e. ,limits at ); intervals where the function is increasing or decreasing; intervals where the graph is concave up or down; in ection points. The y intercept is g(0) = 3 and in this example, there is only one, x0 = 3. Critical points: g(cid:48)(x) = (x2 + 2)2: the x intercepts are the points where g(x) = 0, 2x2 6x + 4 (x2 + 2)2. = 2 x2 + 3x 2 (x2 + 2)2 . The corresponding y-values are y1 = g(x1) 0. 28 and y2 = g(x2) 1. 78, so the critical points on the graph are (approximately) ( 3. 56, 0. 28) and (0. 56, 1. 78) . (ii) the intervals on which g(x) is increasing and decreasing.

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Related Questions

This question explores the quasi-linear utility function. Consider Thomas who has preferences over food, QF, and clothing, QC. His preferences are represented by

U (QF,QC) = [alpha]QF^(1/3) + QC

where [alpha] > 0. Let pF, pC, and I represent the prices of food, clothing, and Thomas's budget for food and clothing.

i. Using the Lagrangian method, solve mathematically for the demand function for each good. Make sure to show each step of your work.

ii. Determine whether food and clothing are normal or inferior goods for Thomas. Prove your answer mathematically.

iii. Are food and clothing substitutes or complements for Thomas? Prove your answer mathematically.

iv. Now assume that [alpha] = 3, and I = $1,224.

1. If pf = $3, and pc = $12 what is Thomas's demand for food and clothing?

2. If the price of food goes down to pf = $4/3, what happens to Thomas's demand for food and clothing?

3. If Thomas’ income falls to $996, what happens to quantity consumed of each good?

4. Graph Thomas's inverse demand curve (i.e price on y-axis, quantity on x-axis) for food when his income is I = $996 and the price of clothing is pc = $12. Be as precise as possible, labeling the exact value of any important points on the graph.

Need assistance with these problems!


1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)
finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.


3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)
unequal to
equal to
linear to
parallel to


4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)
maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.


5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)
same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.


6. The corner point solution method: (Points : 3)
will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.


7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)
1032
1200
360
none of the above


8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)
guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.


9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)
(50,40)
(20,50)
(60,30)
none of the above


10. ____________ is used to analyze changes in model parameters. (Points : 3)
Optimal solution
Feasible solution
Sensitivity analysis
None of the above

PLEASE HELP WITH ONLY THE BOLDED QUESTION THANK YOU

Consider the market for new, single-family homes in New Orleans. The general demand function for new housing in New Orleans is estimated to be Qd =15-2P+0.05M+0.10R where Qd is the monthly quantity demanded, P is the price per square foot, M is average monthly income in New Orleans, and R is the average monthly rent for a three-bedroom apartment in New Orleans. Qd is measured in units of 1,000 square feet per month. 1. New housing in New Orleans is a(n) __________________ (normal, inferior) good. How can you tell from the general demand function? 2. New housing and three-bedroom apartments are _________________ (substitutes, comple- ments) in New Orleans. How can you tell from the general demand function? 3. If average monthly income is $1,500 and the monthly rental rate for three-bedroom apart- ments is $700, then the demand function for new housing in New Orleans is Qd = _____________________________________. 4. Graph the demand curve for new housing in New Orleans on the axes provided below. Label the demand curve D0. 5. What happens to demand when the following changes occur? a. b. c. d. e. The price of the commodity rises. Income decreases and the commodity is normal. Income decreases and the commodity is inferior. The price of a complement good increases. The price of a substitute good decreases. The general supply function for new housing in New Orleans is estimated to be Qs =96+2P-10PL -4PK where P is the price per square foot of new housing in New Orleans, PL is the average hourly wage rate for construction workers, and PK is the price of capital (as measured by the average rate of interest paid on loans to home builders). Qs is measured in units of 1,000 square feet per month. 6. Does it make sense for PL and PK to have negative coefficients in the general supply func- tion? Explain why or why not. 7. If the average hourly wage rate for construction workers is $10 per hour and the average rate of interest on loans to builders is 9 percent (i.e., PK = 9), then the supply function for new housing is Qs = ______________________. 8. Graph the supply curve for new housing in the graph below. Label supply S0. 9. Other things remaining the same, what would happen to the supply of a particular commodity if the following changes occur? a. The price of the commodity increases. b. Government regulators outlaw the use of a technology that enables the good to be produced at a significantly lower cost. c. The prices of inputs used to produce the commodity decrease. d. The price of a commodity that is a substitute in production increases. e. Managers expect the price of the good to fall in the near future. f. As the cost of capital rises, firms in the industry stop purchasing plant and equip- ment, which allows depreciation to diminish the productive capacity in the indus- try. 10. Solve mathematically for equilibrium price and quantity. Show your work: PE = $__________ per square foot. QE = __________ square feet per month (in 1,000s). 11. Do your supply and demand curves intersect at PE and QE found in question 8 above? Should they? 12. In equilibrium found in question 8, compute total consumer, producer, and social surpluses: CS = $____________ PS = $____________ SS = $____________ 13. Suppose New Orleans suffers a serious recession that causes average monthly income to fall from $1,500 to $1,100 per month. If other things remain the same, the demand for new hous- ing in New Orleans is now: Qd = _______________________. Plot this new demand curve in the figure below. Label it D'. 14. Suppose that because of the recession in New Orleans, the wage rate for construction workers falls to $8 per hour. If other things remain the same, the supply of new housing in New Orle- ans is now: Qs = _______________________. Plot this new supply curve in the figure. Label the new supply curve S'. 15. After income falls to $1,100 and wages fall to $8, new equilibrium price and quantity are PE = $__________ per square foot QE = __________ square feet per month (in 1,000s) 16. Determine the effect upon equilibrium price and quantity sold if the following events occur in a particular market: a. The price of a substitute good (in consumption) decreases. b. Consumers’ income increases and the good is inferior. c. Government regulators decide to outlaw a cost-reducing technological process in order to protect the environment. d. The price of a complement good (in production) increases. e. The price of inputs used to produce the good decrease. f. Consumers expect that the price of the good will fall in the near future. g. It is widely publicized that consumption of the good is helpful in prevent- ing cancer. h. The price of a substitute good (in production) decreases. 17. Suppose that a pair of events from problem 15 occur simultaneously. For each of the pairs of events indicated below, perform a qualitative analysis to predict the direction of change in either the equilibrium price or the equilibrium quantity. Explain why the change in one of these two variables is indeterminate. a. Both a and h in problem 15 occur simultaneously. b. Both b and e in problem 15 occur simultaneously. c. Both d and g in problem 15 occur simultaneously. d. Both f and c in problem 15 occur simultaneously.