Demand solutions-1 - Solutions to the homework PDF

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Economics B251, Homework #2 Indiana University Prof. Carl Sanders EXERCISE: Demand Construction The purpose of this exercise is to understand how market demand and supply curves are derived from individual consumer utility functions. Melvin enjoys two activities: racing his bike and buying books, and he will spend $300/wk between these two activities. Bike races cost $50 each to enter and Melvin gets 499 utils from every race. On the other hand, Melvin values books according to the following weekly chart: # of Books 0 1 2 3 4 5 6 7

Total Utility 0 500 900 1200 1400 1500 1550 1550

Marginal Utility — 500 400 300 200 100 50 0

The Deliverables: Please complete each of the following tasks. Provide brief but clear answers. Upload a photo/scan of your answers to the Canvas assignment “In-Class Exercise #2”. Task 1: Fill in the “Marginal Utility” column above. Task 2: How many utils per dollar does bike racing deliver? 499/50 = 9.98 Task 3: How many books should Melvin buy if the price of books is $5? $10? $20? 30, 40, 50, 60? (Assume that Melvin can spend any amount on biking, not just $50 increments, but can only buy whole books.) Let’s make new MU/$ columns in the table, e.g. # of Books

Marginal Utility

MU/5$

MU/10$

MU/20$

MU/30$

MU/40$

MU/50$

MU/60$

0 1 2 3 4 5 6 7

— 500 400 300 200 100 50 0

— 100 80 60 40 20 10 0

— 50 40 30 20 10 5 0

— 25 20 15 10 5 2.5 0

— 16.66 13.33 10 6.66 3.33 1.66 0

—

— 10

— 8.33

10

Since bike racing always gives 9.98 utils per dollar, to maximize utility we want to always spend first on the highest MU/$ goods. We first buy as many books as we can until we get to 10 MU/$, then spend the rest (if any is left over) on biking. So you can see the marked cells giving optimal purchasing of books for each price. Notice that at prices above 50, buying 0 books is optimal since you always get more marginal utility spending on biking. Task 4: Sketch Melvin’s demand curve for books based on what you calculated from Task 3. On a separate graph, sketch the market demand curve if the book market consists of 100 consumers exactly like Melvin. 1

Remember that demand curves (and supply curves) add horizontally, not vertically! Task 5: Suppose the supply for books is given by ten individual sellers, each with the same individual supply curve given by the equation Qs = P. What is the equation of the market supply curve? Add it to your graph of the market demand curve. Market supply curve is given by Qs = 10 P. 2

Task 6: What is the equilibrium market price and quantity of books? Q⋆ = 300, P⋆ = 30. Task 7: What is Melvin’s economic surplus (willingess to pay minus price payed) of him buying his first book in equilibrium? Melvin’s would be happy to buy his first book if the price were as high as $50, but he only had to pay $30 for that book, giving him an economic surplus of $20 on that book. Task 8: To encourage reading, the local government caps book prices at $20. How many books will be bought? Is there excess demand or excess supply? At a price ceiling of $20, there will be 200 total books produced, and presumably all of them will be bought by people willing to pay over $20 for them now. There is excess demand. Task 9: What is the range of economic surplus Melvin might experience in buying his first book now? Two possibilities: Melvin is able to get a hold of a book, in which case he was willing to pay $50 for it but only has to pay $20, giving surplus of $30 which is higher than before! But of course there are 100 people currently each trying to buy 4 books, with only 200 books supplied to the market, so it’s totally possible that for some reason Melvin can’t get one, which would give him economic surplus of $0, significantly worse than before. For example, say the firm just sold first-come first-serve to people in a line. The first 50 consumers would buy 4 books at $20 and be better off than before, but the firm would run out of books and the next 50 people would get nothing. With other selling mechanisms different things might happen, but many people will be left worse off, and it turns out (as we’ll see later) total economic surplus in the market will drop.

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