Microeconomics, IB and IBP

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1 Page 1 of Microeconomics, IB and IBP RE-TAKE EXAM, January 010 Open book, 4 hours Question 1 Suppose that the market demand function for corn is Q d =15 P while the market supply function for corn is Q S =5P.5, both measured in billions of bushels per year. Suppose that the government imposes a $1.40 tax on each bushel of corn. 1.1 What will be the effects on consumer, producer, and aggregate surplus, and what will be the deadweight loss caused by the tax? 1. What is the economic incidence of taxes. Provide an intuition for the resulting tax incidence. Answer: 1.1 We start by inverting the functions given, so that it is easier to draw them. Q d = 15 P = P = Q d Q S = 5P.5 = P =0.5+0.Q S We calculate the equilibrium before taxes. Since demand equals supply, and since at equilibrium Q d = Q S = Q, we write: Q = Q = Q = 10 and thus P =.5 At this price and quantity, the consumer surplus is calculated as the area under the demand function and above the price, while the producer surplus is the area above the supply functions and below the price: CS = PS = (7.5.5)10 =5 (.5 0.5)10 =10 1

2 We now introduce the tax t =1.4. Since the market is competitive, it does not matter where it applies to. Below, we assume that it applies to consumers, and thus it shifts demand function inwards (although we could easily have assumed that it applied to producers, in which case it would have shifted the supply function to the left). P +1.4 = Q d = P =6.1 05Q d Solving for the equilibrium quantity, we get Q d = Q S = Q = 8 Going back to the demand function, we can derive that P =.1 (the producer price) and P +1.4 =3.5 (the consumer price). Calculating the new CS and PS, we have ( )8 CS = =16 (.1 0.5)18 PS = =6.4 At this tax equilibrium there are also tax revenues collected by the government which are equal to TR = tq =1.4 8=11.. Comparing the pre- and post-tax equilibria, we see that total welfare has fallen from = 35 to =33.6. The resulting loss of 1.4(= ) is the so-called deadweight loss (DWL) of taxes. 1.: Tax incidence: that is, who pays the tax: the consumer or the producer? From the above calculations we saw that the consumer paid 3.5 after taxes, while she was paying.5 before taxes were applied. The producer instead, got.1 for its product, while before taxes she was getting.5. Clearly the biggest part of the 1.4 tax is paid by the consumer. More precicely, the consumer pays while the producer pays =0.71, i.e.71% =0.9, i.e.9%

3 of the tax. The intuition for such a result builds on the fact that the agent with the most inelastic function bears the tax heaviest. In the above example, it is the consumer that has the most inelastic function. Question. A local video rental monopoly faces the weekly demand function Q = P. The marginal cost of a rental is $1. Suppose that the town government places a $1 tax on a video rental..1 What effects will the tax have on the price the monopolist charges?. What subsidy would persuade the monopolist to sell the same quantity of rentals that would be sold in a competitive video rental industry? Answer:.1: We first invert the demand function to P =0 Q 50.Given this (inverted) demand function, the marginal revenue has the same slope and double the slope, i.e. MR =0 Q 50 =0 Q 5. Since the monopolist always set MR = MC, the pre-tax equilibrium is characterised by the following quantity and price: 0 Q 5 = 1 = Q = 475 and thus P = 10.5 When taxes apply, the marginal cost of the monopolist will increase bytheamountoftax,i.e. MC =. (one can also assume that the tax falls on the consumers, in which case the demand shrinks inward - such an assumption is also fine - below, I continue with assuming that the tax falls on the producer). The new equilibrium is now 0 Q 5 = = Q = 450 and thus P = 11 Thus, the price the monopolist charges increases..: First of all, we need to find how much it would be produced if the market was perfectly competitive (and without taxes). In that case firms will charge a price equal to their marginal cost, i.e. P =1(=MC). It is then easy to see that Q = =

4 To induce such an output, a subsidy is considered. To find this subsidy, we write MR = MC s = = 1 s = s =19. Thus the subsidy will have to be $19 per rental before a monopoly is induced to produce the competitive output. Question 3 "Competitive firms can easily have profits the real question is for how long they can keep these profits". Discussthisstatement: isittrueorfalse and why? Make sure to develop your arguments both with diagrams and with economic intuition. Answer: The statement is true, if one assumes short run profits not disappearing instantaneously. One should refer to short run(i.e. before entry)and long run (after entry) equilibria that a competitive firm faces. Please see pp at the textbook. It is important to discuss the fact that the theory of perfect competition assumes that entry and exit occurs instantaneously, while in reality such entry and exit takes time, and thus short run profits are not competed away instantaneously. Question 4 Noah and Naomi have decided to start a firm to produce garden tables. If Noah and Noami have at least 500 square meters of garage space, their weekly production is Q = L, where L is the amount of labour they hire, in hours. The wage rate is $1 an hour, and a 500 square-meter garage rents for $50 per week. 4.1 What is the weekly cost function for producing garden tables? Graph it. After some time Noah and Noami want to expand. They now want to produce 100 garden benches per week in two production plants A and B. AssumethatthecostfunctionsatthetwoplantsareC A = 6000Q A 3(Q A ) and C B = 650Q +(Q B ). 4. What is the best assignment of output between the two plants? (that is, how many to produce at A and how many at B). 4

5 Answer: 4.1: The weekly cost function has two elements; the variable cost and the fixed cost. The variable refers to the workers hired, while the fixed to the rent paid for the garage space. Thus TC = w L + F = = 1 L + 50 To find the demand for labour (L), i.e.how many workers Noah and Naomi will want to hire, we solve Q = L = L 1 as L = Q. Thus, the cost function (i.e. total costs as a function of output) is TC =1 Q + 50 We can easily graph such a function in the figure below. TC 50 4.: There is typo in the exam question. The cost function of plan B should be C B = 650Q B +(Q B) and not C B = 650Q +(Q B ). While some assumed that, some assumed that it should have been C B = 650Q B +(Q B ) and did their calculations based on that. No matter what, I graded the calculations and reasoning given the assumption that the student has chosen, and not the actual result. Below, I present the answer key for the C B = 650Q B +(Q B). In order to solve for the best assignment of outputs, we know that the equilibrium should be characterised by MC A = MC B,i.e. themarginal costs should be the same in both places. Thus we have MC A = Q A = 1304Q B = MC B 5 Q

6 Given that Q A + Q B = 100, wewrite (100 Q B ) = 1304Q B which implies that Q B =7.6 and Q A =9.4. 6