Econ 201 Fall 2011 Exam 2

# Econ 201 Fall 2011 Exam 2 - ECONOMICS 201 FALL 201 1 EXAM 2...

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Unformatted text preview: ECONOMICS 201 FALL 201 1 EXAM 2 Instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total, Each question is worth 5 points unless indicated otherwise. 1. Characterize the returns to scale (decreasing, constant, or increasing) associated with the following production functions. a. y=f(X)=5X 19- y: f(X1:X2) =mjn{2X1’X2}+X105 2. True or false: If proﬁt is inﬁnite and there are no ﬁxed costs, the production function can be IRS or CRS, but if profit is inﬁnite and there are ﬁxed costs, then the production function must be IRS. Explain your answer with one or two sentences and/ or a graph. 3. True or false: If there are no ﬁxed costs, it is optimal for a competitive ﬁrm to produce no output when output price is above average cost. Explain your answer with one or two sentences and/ or a graph. 4. Tiger Mom’s production function is y = f(X1,X2,X3) = IninijlﬁX2 ,lOXS}. Prices are w1 =1, w2 = 2 , and w3 = 3 . Suppose that the required level of output is; = 50. (10 points) a. How much is she spending at the optimal input bundle in the short-run when E = 10 ? b. How much is she spending at the optimal input bundle in the long—run? 5. Chipotle produces burritos (output y) using only “yummy goodness” (input X). Burritos are valued at price P in the market, and the input price is w. Chipotle’s production function is y = f (X) z X "‘ , where 0<a<1. (10 points) a. What is Chipotle’s PMP? b. What is the FCC? c. What is the factor demand function? d. Taking a partial derivative, Show that the production of burritos (output) decreases when the price of yummy goodness (input price) rises. 6. Let’s continue the above Chipotle example. (10 points) a. What is Chipotle’s CMP? Suppose that the required level of output is; . b. What is the conditional factor demand function? c. What is the cost function? Hint: Your answer should be an expression involving w, }, and a . 7. Dooley’s production function is y = f (X 1 , X 2) 2 ().5X1 + 2X 2 . Output price is P, and input prices are w1 ande , respectively. (10 points) a. What is Dooley’s PMP? b. What are the conditions that ensure profit is inﬁnite? 8. Multiple choice. Given the graph, at which price would a competitive ﬁrm produce a positive amount of output but obtain negative proﬁts? (Please circle one response.) Graph 15., Guésh'nn ! ML a. Price A b. Price B S; Ct Price C d. Price D 9. Alexa’s cost function is C(y) = y2 + 2y + 4. (10 points) A B a. Above what price does Alexa choose to produce? C V b. Below what price does she obtain negative proﬁts? 10. Based on the Utility Possibility Set, clearly label the points corresponding to the Pareto Set (all PO allocations). bl; . . ‘4- \ ll. Bert and Ernie are competitive consumers in a pure exchange economy. Their endowments of good 1 and 2 are em”! = (5,5) and em”? = (5,5) . The prices of goods 1 and 2 are P1 and P2 . Bert’s demand function for good 1 is X13“ 2 11:51:” . Erme’s demand function for good 1 is X 15m” = 1:?” . (10 pomts) l l a. What is the aggregate amount of good 1? b. What are W135” and mEmza (as a function of prices and endowments)? c. Normalize R = 1. What are the equilibrium prices, i.e. what is P2 ‘? 12. Suppose there are two competitive consumers in the economy, A and B. They have utility functions uA(X1A,X2A) = X345ng and uB(XIB,XZB) = XPEZXSJ'S. There is aﬁxed amount ofeach good, X1 and Z. (15 points) a. In a competitive equilibrium, each consumer’s MRS equals the price ratio, which implies that A’s MRS equals B’s MRS. What is the expression MRS A 2 MRS B ? b. We Wish to derive an expression for Pareto Optimality. To obtain this, let’s maximize A’s utility subject to B’s utility held constant at us. What are the FOCs with respect to X 1 A and X 2 A ? Hint: Prior to taking derivatives, plug in the following: X13 2 X1 — X 1 A and X 2 B 2 f2 — X 2 A . c. Every competitive equilibrium is Pareto Optimal. Show that the FOCs in part b yield the same expression as in part a. Hint: Remember that XEB = X1'“ X],I and X2,3 = R2 — XZA. ...
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Econ 201 Fall 2011 Exam 2 - ECONOMICS 201 FALL 201 1 EXAM 2...

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