ECON UN3213-Intermediate Macroeconomics

Assignment

Problem 1

Suppose you have 8 used Varian’s Intermediate Micro textbooks, which you want to get rid of. There are 8 potential buyers who are willing to buy your used textbooks. You know how much each potential buyer is willing to pay for a single book. Let’s call this amount the reservation price. Reservation prices of potential buyers are in the table.

Buyer

(For example, buyer A is willing to pay at most 40 dollars for a single book.)

(a)If you offer all your books at the same price of $20, which buyers will buy the books?

(b)If you offer all your books at the same price of $20, what is consumer A’s net consumer’s surplus?

(c)If you offer all your books at the same price of $20, what is consumer B’s net consumer’s surplus?

(d)If you offer all your books at the same price of $20, what is the total net consumers’ surplus generated in the market?

(e)If you sell all your books at the same price of $20, what is the total gross consumers’ surplus generated in the market?

(f)If you lower the sale price of your books to $19, by how much does the total net consumers’ surplus increase?

(g)If you lower the sale price of your books to $19, by how much does the total gross consumers’ surplus increase?

Problem 2

Suppose Lizzie’s demand function for cherries is D p 10 p, where p is the price of a pound of cherries.

(a) If the price of a pound of cherries is $6, how many pounds of cherries will Lizzie buy?

b) How much gross consumer’s surplus does Lizzie get from consuming cherries at the price of $6 per pound?

(c)How much money does Lizzie spend on the cherries?

(d)What is Lizzie’s net consumer surplus from consuming cherries at the price of $6 per pound?

 

Problem 3

In the city of Johor Bahru in Malaysia, the locals’ demand function for beets is ql ? max?200 ?p,0? and the tourists’ demand function for beets is qt ? max?90 ? 4p,0?. (a) What is the locals’ price elasticity of demand for beets at price p?

(b)What is the tourists’ price elasticity of demand for beets at price p?

(c)At what price is the locals’ price elasticity of demand for beets equal to -1?

(d)At what price is the tourists’ price elasticity of demand for beets equal to -1?

(e)Draw the locals’ demand curve for beets, the tourists’ demand curve for beets, and the market (locals’ and tourists’) demand curve for beets. Use different color for each curve.

(f)At what non-zero price there is a kink in the total demand curve?

(g)What is the market demand function for prices below the kink?

(h)What is the market demand function for prices above the kink?

(i)At what price the price elasticity of market demand is -1?

(j)At what price will the revenue from the sale of beets be maximized?

(k)If the goal of sellers of beets to maximize revenue, will beets be sold to locals only, to tourists only, or to both?

Problem 4

The demand function for football tickets for a typical game at OSU is

D p 200,000  10,000p. OSU has a clever athletic director who has mastered Intermediate Micro and sets ticket prices so as to maximize revenue. The Shoe, where football games are held, has capacity of 100,000 people. (a) What is the inverse demand function?

(b)Write an expression for total revenue as a function of the number of tickets.

(c)Write an expression for marginal revenue as a function of the number of tickets.

(d)Use different colors to draw the inverse demand function and marginal revenue.

Also, draw a vertical line representing the capacity of the stadium.

(e)What price will generate the maximum revenue?

(f)How many tickets will be sold at this revenue-maximizing price?

(g)What is the marginal revenue at the revenue-maximizing quantity?

(h)What is the price elasticity of demand at the revenue-maximizing price?

(i)Will the stadium be full at the revenue-maximizing price?

(j)A series of winning seasons causes the demand curve for football tickets to shift upward. The new demand curve is D?p? ? 300,000 ? 10,000p. What is the new inverse demand function?

(k)What is the marginal revenue for the new demand function as a function of the number of tickets?

(l)Draw the new inverse demand function and the new marginal revenue using different color.

(m)Ignoring stadium capacity, what price would generate maximum revenue?

(n)How many tickets will be sold at this new revenue-maximizing price?

(o)If the athletic director wanted to maximize revenue, how many tickets will he actually sell and at what price?

(p)What is the marginal revenue from selling an extra ticket at this new price?

(q)What is the price elasticity of demand for tickets at this price?

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