# econ101_ps4 - METU Department of Economics Econ 101...

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1 METU Department of Economics Econ 101: Introduction to Economics I All sections (01-02-03) Fall 2010 PROBLEM SET 4 PART A- PROBLEMS 1. The table below gives the demand schedules for good A when the price of good B (P B ) is 8 YTL and 12 YTL. Complete the last column of the table by computing the cross elasticity of demand between goods A and B for each of the three prices of A. Are A and B complements or substitutes? P B = 8 YTL P B = 12 YTL P A Q A Q’ A Elasticity ( ε ) 8 2000 4000 7 4000 6000 6 6000 8000 2. a) Calculate price elasticity of demand for the following functions when P=8 and when P=6. b) Calculate the arc elasticity of demand between P=6 and P=8 for (ii) i. P = 40 – 0.5Q ii. Q = -4 + 0.75P iii. 4Q + 4P = 64 3. The market demand and supply functions for a commodity is given below: Q d = 100 – 2P Q s = -20 + 4P a) Find the equilibrium price and quantity. b) Find the point elasticity of demand and supply at the equilibrium. c) Find the price and quantity where price elasticity of demand is unitary. d) Find the maximum expenditures by consumers (TR) given their demand.

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2 4. The following table shows the price and yearly quantity of T-shirts according to average income. T-shirt price Quantity demanded (average income is \$20,000) Quantity demanded (average income is \$30,000) \$4.50 2,400 3,600 \$5.50 1,600 2,800 \$6.50 800 2,400 \$7.50 400 1,800 a) Calculate the price elasticity of demand (using the midpoint method) when the price of T-shirts rises from \$4.50 to \$5.50, when average income is \$20,000. b) Calculate the income elasticity of demand (using the midpoint method) when average income increases from \$20,000 to \$30,000, when the price of a T-shirt is \$4.50. 5. Use the given monthly information in the table to answer the questions below. Month Income Demand for beef Demand for chicken 1 \$400 5 pounds 3 pounds 2 \$800 3 pounds 5 pounds 3 \$800 5 pounds 3 pounds a) Calculate the income elasticities of demand for beef and chicken and specify the kinds of goods they are in months 1 and 2? b) In Month 3, the price of chicken rose from \$2.00 per pound to \$3.00 per pound. What is the cross-price elasticity of demand for beef? Are beef and chicken complements or substitutes? 6. Suppose that Mrs. Stewart allocates all her income on food and shelter. The price of food is 5 YTL and the price of shelter is 8 YTL per unit. Suppose further that the following equations represent the marginal utilities of food and shelter, respectively. MU F = 35 – 5F MU S = 44 – 4S where F and S represent the quantity of food and shelter consumed, respectively and MU F and MU S are measured in million utils. If Mrs. Stewart’s income is 39 YTL, how many units of each good should she purchase to maximize her total satisfaction?
3 7. A consumer has an income of 150 YTL per month and he wishes to spend all of it on two goods X and Y, whose prices are 5 and 7.5, respectively. a)

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econ101_ps4 - METU Department of Economics Econ 101...

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