Practice Midterm Exam Microeconomics: 33001 Professor Owen Zidar This exam is comprised of 3 questions. The exam is scheduled for 1 hour and 30 minutes. This is a closed-book, closed-note exam. There is a formula sheet attached to the final page of the exam for your reference feel free to rip it off. Write all of your answers in Blue Books, and carefully number your answers so that it is clear which question you are answering. PLEASE SHOW ALL OF YOUR WORK! If we cannot tell how you arrived at an answer, you may not receive full credit. An answer with no justification may receive no credit. You must read and sign the following pledge. If you do not read and sign the following pledge, your exam may be treated as if you did not turn it in. Turn in this exam with your Blue Book once the exam is complete. Honor Code: I pledge my honor that I have not violated the Honor Code during this examination. X Print your name:
1. SHORT ANSWER (40 points) State whether the following statements are TRUE, FALSE, or UNCERTAIN. You can take the non-italicized portions as given. For each of these problems, you must explain your answer with words, math, and/or pictures. The quality of the explanation is a substantial part of the grade. (a) Jill receives a $10,000 per year scholarship to go to college. Jack is offered no financial aid of any kind. College tuition is $25,000 per year, and college lasts four years. If both Jack and Jill decide to go to college, Jack s marginal willingness to pay for college must be greater than Jill s marginal willingness to pay for college. (b) A decrease in the price of capital reduces employment. (c) If, at your current consumption levels, your marginal utility for baseball tickets is higher than your marginal utility for football tickets, then you should go to more baseball games and less football games. (d) A plot of data regarding the price and quantity sold of ski lift tickets in Wisconsin over the past five years is presented below. These observations demonstrate that skiing in Wisconsin is a Giffen good during the time period indicated.
2. Consumer Theory (30 points) Consider an economy with two goods: cigarettes (C) and alcohol (A). The typical consumer s preferences are summarized by the utility function: U(A, C) = 3A + 3AC + 4C where A is the number of alcoholic drinks consumed in a month and C is the number of packs of cigarettes consumed in a month. The typical consumer sets aside $102 to spend on cigarettes and alcohol. The price of cigarettes is $2 per pack; the price of alcohol is $3 per drink. (a) On a graph with alcoholic drinks on the x-axis and cigarettes on the y- axis, draw the budget constraint. What is the slope of the budget line? (b) On the same graph draw an indifference curve that goes through the point representing the optimal consumption bundle. Label the optimal bundle. Without doing any calculus, what is the Marginal Rate of Substitution between cigarettes and alcoholic drinks at the optimal consumption bundle? (c) Write out the equation (in terms of C and A) for the Marginal Rate of Substitution between cigarettes and alcoholic drinks? (d) How many alcoholic drinks and how many packs of cigarettes will the typical consumer purchase in a typical month? (e) A tax on alcohol raises the price to $6. How many alcoholic drinks will the typical consumer purchase in a month now? (f) Based on your answers, give an estimate of the price elasticity of demand for alcoholic drinks.
3. Supply and Demand (30 points) Market supply and demand for gasoline are: Q = 100 + 30P Q = 500 20P where P is the price per gallon and Q is the quantity in gallons. (a) On a graph with price on the vertical axis and quantity on the horizontal axis, draw the supply and demand curves. Label points where each curve hits the vertical and horizontal axes. What are quantity and price in equilibrium? (b) How much is total consumer surplus? (c) The government introduces a price ceiling of 5 dollars per gallon. gasoline is bought and sold? (d) Is there a surplus or shortage? How great is that surplus, or shortage? How much (e) What is consumer surplus now that the price ceiling is in effect? You may ignore income effects. Are consumers as a group made better or worse off by the price ceiling? Why? (f) The surplus/shortage you uncovered in part (d) leads to a political backlash against the price ceiling. After repealing the price ceiling law, the government decides instead to subsidize the supply side of the market. As a result of this new policy, producers will receive S dollars for each unit of gasoline that they produce and sell. [Hint: This will lead to a shift down of the supply curve of S dollars.] The government wants the equilibrium price paid by consumers, net of the subsidy, to be 5 dollars. What should the government subsidy rate (S) be to make this happen? Is this amount more or less than $3? Why?
Formula Sheet Elasticity Taxes Price Elasticity (of Supply or Demand) is % Q % P, calculated in two ways. Point Elasticity: ε = P Q dq dp Arc Elasticity: (Q 2 Q 1 )/( 1 2 Q 1+ 1 2 Q 2) (P 2 P 1 )/( 1 2 P 1+ 1 2 P 2) Cross price elasticity of demand: 1 ε D other = P other Q D Income elasticity of demand: 2 ε D income = M Q D Q D M Q D P other where M is income. Let P D be the consumer s (demander s) price, and P S be the firm s (supplier s) price Tax of $t per unit: P D = P S + t Sales tax of τ per dollar sold: P D = (1 + τ)p S Tax incidence: Consumers pay a share ε S ε S + ε D, producers pay ε D ε S + ε D Consumer Theory Consumer s Problem: max U(x, y) subject to p Xx + p Y y M x,y Marginal utility: MU X = du dx, MU Y = du dy Marginal Rate of Substitution: MRS = MU X MU Y Optimal Consumption: Firm Behavior MRS = p X p Y, or equivalently MU X p X Profit = Revenue Costs = P Q C(Q) = MU Y p Y For inverse demand curve P (Q), revenue is Rev(Q) = Q P (Q). Marginal Revenue: MR = d dq Rev(Q) = P (Q) + QP (Q) Marginal Costs: MC = d dq C(Q) Profit maximization condition: MR = MC 1 This shows the point elasticity. Assume you have an equation for a demand curve which involves not only the price of the good but also the price of some other good (e.g., Q = 10 3P + 2P other ). 2 This shows the point elasticity. Assume you have an equation for a demand curve which involves not only the price of the good but also income (e.g., Q = 10 3P + 2M).
Math Formulas Area of a rectangle: base height Area of a triangle: 1 2 base height d Derivative of a polynomial: dx (a xb ) = a b x b 1 for constants a and b Derivative of ln: d ln x dx = 1 x