ECON 1530 Lecture Notes - Lecture 3: Power Rule, Tax Rate, Implicit Function

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17 Nov 2017

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Recall the power rule d dx xn = nxn 1. = g(x) g(x) + g(x) d dx g(x) [g(x) g(x)] d dx d dx g(x) [g(x) g(x) g(x)] d dx g(x) + g(x) g(x) d dx g(x) g(x) = 3[g(x)]2 d dx g(x) and more generally: y = [g(x)]a y = a[g(x)]a 1g (x) 1 or in leibniz"s notation, y = ua dy dx. 2 (cid:2) (cid:3)(cid:4) (cid:5: t = a (by + c)p + ky. T = aup + ky, up 1 u = (by + c) du dy. = abp (by + c)p 1 + k. Think of: y = [g(x)]a = ua u = g(x) Suppose y is a function of u and u is a function of x then y is a function of x, called a composite function. Suppose x changes u changes y changes; this is a chain reaction the derivative of y with respect to (wrt) x re ects this.

Related Questions

2. Now you are told that the economy is producing efficiently and has chosen to produce and consume 8 units of X. At this point on the production possibilities frontier, you can use calculus to obtain the opportunity cost of Y as: A) 2 B) 1/2 C) D) 3/2 E) 2/3 F) 3 G) 1/3 H) 4 1) 1/4 J) 8/3 K) 3/8 L) 5/2 M) 2/5 N) 4/3 0) 3/4 P) 6 Q) 1/6 R) 8 S) 1/8 T) none of the above

1. Suppose the price of x₁ is $20 and the price of x₂ is $4. If good x₁ is on the horizontal axis, what is the slope of the consumer's budget constraint?

a. -0.20

b. -0.25

c. -5.0

d. -0.2

e. -4.0

f. -20.0

2. Suppose the price of x1 is $5 and the price of x2 is $1 and Toni's income is $20. Suppose Toni gets a $5 gift card that can only be used for the purchase of x1 and there is no resale value of the gift card. With the gift card, the commodity bundle (1,20) is on Toni's budget constraint.

True

False

3. Tiffany's utility function is given by the formula U(x1, x2) = min{20x1, 10x2}. If x1 = x2, which commodity will have a greater marginal utility?

A. Both x1 and x2 have the same marginal utility

B. It is not possible to determine which commodity has higher marginal utility

C. x2

D. x1

4. For U(x₁,x₂) = 6x₁^1/3 + x₂, preferences are

a. consistent with diminishing marginal rate of substitution.

b. consistent with constant marginal rate of substitution.

c. consistent with increasing marginal rate of substitution.

d. not consistent with a utility function.

5. For a utility function of the form U(x₁,x₂)=min{5x₁,10x_2}, the individual will have excess x₂ for commodity bundles where

a. x2>2x1 b. x2>5x₁

c. x₂>0.5x₁ d. x2>10x₁

6. Matt enjoys Fuji and Gala apples and finds 1 Fuji apple to be just as good as 4 Gala apples.

a. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=0.25F+G

b. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=F+4G

c. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+.25G

d. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+G

e. Both A and B

f. Both C and D

amaranthelk637

The Modified Keynesian Model

Y = C + I + G + X â IM â¦ equilibrium condition in a 4-sector model where:

C = 150 + 0.9DI â¦ consumption function

I = 50 â¦ autonomous investment

G = 100 â¦ autonomous government spending

X = 200 â¦ autonomous exports

IM = 100 â¦ autonomous imports

And also:

DI = Y â T + Tr T = 0 â¦ autonomous taxes

Tr = 0 â¦ autonomous transfer payments

YF = 5000 â¦ full-employment Y

1. Solve for the equilibrium level of real output/income (Y*) in this economy.

2. Given the model above, net exports equal $________. Does this represent a trade deficit or trade surplus?

3. Given the model above, the federal budget has a (deficit/surplus) equal to $________.

4. What is the value of the MPC? â¦ the value of the MPS?

5. Calculate the âoversimplifiedâ expenditure multiplier.

6. Suppose that full-employment (YF) equals $5000. Is there a recessionary or inflationary output gap?

7. (Refer to question â6â.) How much is the gap equal to?

8. Suppose the government chooses to eliminate the gap by using expansionary fiscal policy (i.e., increasing G). Given the numbers above, by how much would government spending (G) need to increase to achieve the goal of full-employment?

9. Suppose instead that the government decided to lower taxes to eliminate the output gap in question â6â. How much would taxes need to fall to achieve the goal of full-employment?

10. Which action (raising G or lowering T) has the largest effect on the federal budget deficit and the national debt?

11. Suppose the national debt equaled $6000 before the tax cut (refer to question â9â). What would be the value of the national debt after this policy action?

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ECON 1530 Lecture Notes - Lecture 3: Power Rule, Tax Rate, Implicit Function

ECON 1530 Full Course Notes

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