# Consider perfect complements type of preferences

we are still looking for your answers.. (10 points) Consider perfect complements type of preferences. (i) Can an increase in the price of good 1 lead to an increase in the demand for good 2? Illustrate your answer on the x1,x2 plane (figure) and explain. (30 points) Consider the utility function u = 2(x1)0.5 + x2. (i) Obtain the demand function for good 1 and the demand function for good 2 (show all your steps). (ii) Fix the price of good 2 at p2 = 10. If income is m = 20 and p1 = 2, what are the quantities of good 1 and good 2 demanded (warning: possibility of corner solution)? (iii) Same question as (ii), but income becomes m = 200. (iv) Suppose p2 = 10 is constant but p1 = 4. What income mIdoes the consumer need to be able to buy the quantities you found in part (iii)? (v) What are the optimal quantities of good 1 and good 2 demanded when p1 = 4, p2 = 10 and income is the mI you found in (iv)? (vi) Now, show on a figure the income and substitution effects on good 1 for an increase in p1 from 2TL to 4TL, using the numerical answers you found above. Pay attention to the shape of indifference curves and budget lines. (20 points) A consumer has monotonic and strictly convex preferences, but given her m and p2, good 1 is a Giffen good. Illustrate on the x1,x2 plane (figure) what happens to the demand for good 1 when its price increases. Decompose the total impact on the demanded (optimal) x1 into its substitution and income effects on your figure (clear figures please). 4. (10 points) On page 160 of our textbook the author writes: “The substitution effect is sometimes called the change in compensated demand.” What is the compensation for, and why is it needed? 5. (15 points) You consume 5kW of electricity at the current price of 1TL/kW. The electricity distributor makes you the following offer: “your electricity price will be 3TL/kW, but we shall deduct from (reduce) your bill 10 TLs (.(3-1))” Suppose there are two goods, electricity (good 1) and other goods (good 2). Show your original (initial) consumption by drawing a budget line and an indifference curve. Will you (a) take the distributor’s offer, or (b) will you reject it and continue to consume electricity at the price 1TL/kw? Illustrate your answer on the same figure and explain why you chose (a) or (b). 6. (15 points) Why isn’t there any income effect for a consumer whose preferences are of the perfect substitutes type, like U = x1 + x2? Draw the relevant figure and explain carefully, to show that you understand the nature of income and substitution effects on demand when own price increases)

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