ECO 305 Study Guide - Quiz Guide: Partial Derivative, Economic Equilibrium, Demand Curve
1. Take the derivative of the following functions with respect to X
a. Y = X4 + 3X 2 + 2X + 5 = 4(X)^3+2*3(X)+2(0)+(0)=4x3+6x+2
b. Y = X2* X2 (Use the product rule—do not simplify the equation)
=x4=4x3
c. Y = (4X2 + 3X )/ 3X3
=(-4x2+6x)/3x4
2.a. U = X2 + Y2 take partial derivative with respect to X then take partial derivative with respect to Y.
This will give you the marginal utility of X and the marginal utility of Y. Are the marginal utilities
increasing, decreasing or constant?
U(x)=2x, U(y)=2y The marginal utilities are constant.
b. U = X2 * Y2 take partial derivative with respect to X then take partial derivative with respect to Y Are
the marginal utilities of X and Y increasing, decreasing, or constant?
U(x)=2xy2, U(y)=x22y The marginal utilities are increasing.
Review of Supply and Demand:
a. Economists predict a recession starting next year. What will happen to the price and quantity of a
typical good sold at Walmart?
Due to the anticipated recession, demand for goods would decrease at each price level. Therefore,
demand curve would shift to left which means price and quantity will fall.
b. Economists predict a recession starting next year. What will happen to the price and quantity of a
typical good sold at Tiffany’s?
Due to the anticipated recession, demand for jewelry would decrease at each price level. Therefore,
demand curve would shift to left. As a result, the price and quantity will decrease. Since, Tiffany sells
luxurious goods the effect of recession would take a large toll on revenue.
c. The price of steel is expected to go down 2% next year while automobile worker wages are expected
to rise 10%. What will happen to the price and quantity of automobiles sold?
Due to these expected changes, supply of automobiles will decrease but the price will increase. Resulting
in supply curve shifting to right, but due to increase in wages, cost would increase resulting in supply
curve shifting to left.
d. The president of the United States announces federal action designed to increase regulation and limits
in the gun market. What will happen to the equilibrium price and quantity of gums?
Due to the regulations and limits, demand for guns will decrease which will lead to a drop-in supply
resulting in a decrease in price and quantity.
e. The FDA introduces a $2 tax on fast food but NOT on drinks. What will happen to the equilibrium
price and quantity for coca-cola?
Since most people consume coca cola as a complement with fast, the decrease in fast-food consumption
will reduce demand for coca cola. Therefore, a left shift in demand curve leading to decrease in price and
quantity demanded.
f. The price of sugar increases. What happens to equilibrium price and quantity of coca-cola? What
happens to equilibrium price and quantity of diet coke?
With the price of sugar increases which leads to the cost of production of a regular coke increases, so its
supply decreases at each price. The supply curve drops towards left. As a result, the price increase and
quantity demanded decreases.
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Document Summary
Take the derivative of the following functions with respect to x, y = x4 + 3x 2 + 2x + 5 = 4(x)^3+2*3(x)+2(0)+(0)=4x3+6x+2, y = x2* x2 (use the product rule do not simplify the equation) =x4=4x3: y = (4x2 + 3x )/ 3x3. U = x2 + y2 take partial derivative with respect to x then take partial derivative with respect to y. This will give you the marginal utility of x and the marginal utility of y. Review of supply and demand: economists predict a recession starting next year. Due to the anticipated recession, demand for goods would decrease at each price level. Therefore, demand curve would shift to left which means price and quantity will fall: economists predict a recession starting next year. Due to the anticipated recession, demand for jewelry would decrease at each price level. As a result, the price and quantity will decrease.
