Calculate the equilibrium price and quantity
Macroeconomics
1. For each sentence below describing changes in the tangerine market, determine whether the statement is true, false, or uncertain. Explain your answer and illustrate it with a graph. (10′)
a) If consumer income increases and worker wages fall, quantity demanded will rise and prices will fall.
b) If the price of canning machinery increases and the growing season is unusually cold, quantity demanded and price will both fall. (Hint: canning machinery is a complement to tangerine.)
2. Consider the following demand and supply relationships in the market for golf balls: Qd = 90-2P-2T and Qs = -9+5P-2.5R, where T is the price of titanium, a metal used to make golf clubs, and R is the price of rubber.
a) If R=2 and T=10, calculate the equilibrium price and quantity of golf balls.
b) At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply.
c) At the equilibrium values, calculate the cross-price elasticity of demand for golf balls with respect to the price of titanium. What does the sign of this elasticity tell you about whether golf balls and titanium are substitutes or complements?
3. Draw indifference curves to represent the following types of consumer preferences (Put peanut butter on the horizontal axis and jelly on the vertical axis). For each case, draw two curves U1 and U2 (with U2>U1) and illustrate the preference direction.
a) I like both peanut butter and jelly, and always get the same additional satisfaction from an ounce of peanut butter as I do from 2 ounces of jelly.
b) I like peanut butter, but neither like nor dislike jelly.
c) I like peanut butter, but dislike jelly.
d) I like peanut butter and jelly, but I only want 2 ounces of peanut butter for every ounce of jelly.
e) I like to put both peanut butter and jelly on my toast. I can change the mix of peanut butter and jelly. However, one cannot completely replace the other.
4. Janice Doe consumes two goods, X and Y. Janice has a utility function given by the expression:
1695_Calculate the price elasticity of demand.png The current prices of X and Y are 25 and 50, respectively. Janice currently has an income of 750 per time period (Put X on the horizontal axis and Y on the vertical axis).
a) Is the assumption that “more is better” satisfied for both goods?
b) Calculate MRSX,Y. Determine if it is diminishing for this utility function.
c) Express the budget equation mathematically.
d) Draw a graph to illustrate the shape of a typical indifference curve. Label the curve U1. Does the indifference curve intersect either axis? On the same graph, draw a second indifference curve U2, with U2>U1.
e) Determine the values of X and Y that will maximize utility in the consumption of X and Y. Illustrate your answer on a graph.
f) Determine the total utility that will be generated for this individual.
5. Consider a consumer with the utility function U(x, y) = min(3x,5y), that is, the two goods are perfect complements in the ratio y:x= 3:5. The prices of the two goods are Px=$5 and Py=$10, and the consumer’s income is $220. Write the consumer’s budget constraint, determine the optimum consumption basket and show it graphically (Put X on the horizontal axis and Y on the vertical axis).
6. Paul consumes only two goods, pizza (P) and hamburgers (H) and considers them to be perfect substitutes, as shown by his utility function: U = P + 4H. The marginal utilities are MUp = 1 and MUH = 4. The of Pizza is $3 and the price of pizza is $3 and the price of hamburgers on the, and Paul’s monthly income is $300 (Put pizza on the horizontal axis and hamburgers on the vertical axis).
a) Express the budget equation mathematically.
b) Find the optimal combination of X and Y that will maximize Paul’s utility.
c) Knowing that he likes pizza, Paul’s grandmother gives him a birthday gift certificate of $60 redeemable only at Pizza Hut. Though Paul is happy to get this gift, his grandmother did not realize that she could have made him exactly as happy by spending far less than she did.
How much would she have needed to give him in cash to make him just as well as off as with the gift certificate? Illustrate your answer on a graph.
