ECO300.Intermediate Microeconomics. Mathematics & Economics Coursework

ECO 300.Intermediate Microeconomics
Homework 1
1. Consider a demand of the form QD = 2P + 16 and a supply curveof the form Qs = P  5. Plot these curves and be sure to P on the verticaland Q on the horizontal axis. Find the equilibrium price and quantity.2. Consider the function Y =
pXZ where X > 0 and Z > 0. Draw thecontour lines (in the positive quadrant) for this function for Y = 4, Y = 5,and Y = 10. What do we call the shape of these contour lines? Where doesthe line 20X + 10Z = 200 intersect with the contour lineY = 50?3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P; C) = 4C + 5P. What does her utility function say about her MRSof Coke for Pepsi? What do her indi§erence curves look like? What typeof goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 andMary has $20 to spend on these products, how many units of each productshould she buy in order to maximize her utility? Show this utility maximizing combination combination of Pepsi and Coke on the graph. how wouldher consumption and utility maximizing bundle of Coke and Pepsi changeif the price of Coke decreases to 50 cents.4. Suppose a person has $8 to spend only on apples and bananas. Applescost $0:4 each, and bananas cost $0:1 each. Furthermore, his preferences forapples (A) and bananas (B) can be represented by U =pAB.a) If A = 5 and B = 80, what will utility be?b) If A = 10, what value of for B will provide the same utility in part a?c) If A = 20, what value of for B will provide the same utility in partsa and b?d) Graph the indi§erence curve implied by parts a through c.e) Give the budget constraint, which of the points identiÖed in parts athrough c can be bought by this person?f) show through some examples that every other way of allocating incomeprovides less utility than does the point identiÖed in part b. graph this utilitymaximizing situation.5. Vera is an impoverished graduate student who has only $100 a monthto spend on food. She has read in a government publication that she canassure an adequate diet by eating only peanut butter and carrots in the Öxedratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides tolimit her diet to that regime.a) If peanut butter costs $4 per pound and carrots cost $2 per pound,how much can she eat during the month?b) Suppose peanut butter costs rise to $5 because of peanut subsidies2introduced by a politically sensitive government. By how much will Verahave to reduce her food purchases?c) How much in food stamp aid would the government have to give Verato compensate for the e§ects of peanut subsidy?d) Explain why Veraís preferences are of a very special type here. Howwould you graph them?

Eco 300 Intermediate MicroHomework 21.

Suppose David spends his income (I) on two goods, x and y, whose marketprices are px and py, respectively. His preferences are represented by the utilityfunction u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y).a. Derive his demand functions for x and y. Are they homogeneous inincome and prices?b. Assuming I = $60 and px = $1, graph his demand curve for y.c. Repeat part (b) for the case in which px = $2.2. David gets $3 per week as an allowance to spend any way he pleases.Since he likes only peanut butter and jelly sandwiches, he spends the entireamount on peanut butter (at $0.05 per ounce) and jelly (at $0.1 per ounce).Bread is provided free of charge by a concerned neighbor. David is a picky eaterand makes his sandwiches with exactly 1 ounce of jelly and 2 ounces of peanutbutter. He is set in his ways and will never change these proportions.a) How much peanut and jelly will David buy with his $3 allowance perweek?b) Suppose the price of jelly increases to $0.15 per ounce. How much of eachcommodity would be bought?c) By how much should David’s allowance be increased to compensate forthe rise in the price of jelly in part b?d) Graph your results of part a through part c.1e) In what sense does this problem involve only a single commodity? Graphthe demand curve for this single commodity.f) Discuss the results of this problem in terms of the income and substitutioneffects involved in the demand for jelly.3. Consider the function y = 2x2 + x for which dy/dx = 4x + 1. Calculatethe elasticity of y with respect to x at x = 2.4. In order to reduce farm output, raise farm prices, and thus raise farmincomes (revenues), the government pays farmers to set aside a portion of theirland from production. Using a graph, explain in terms of the elasticity ofdemand for farm products why farmers may be better-off when harvests are loweven if we ignore the money they receive from the set-aside program.5. Suppose the quantity of good X demanded by individual 1 is given byX1 = 10 − 2PX + 0.01I1 + 0.4PYand the quantity of X demanded by individual 2 isX2 = 5 − PX + 0.02I2 + 0.2PYa) What is the market demand function for total X (= X1+X2) as a functionof PX, I1, I2, and PY .b) Graph the two individual demand curves (with X on the horizontal axis,PX on the vertical axis) for the case I1 = 1000, I2 = 1000, and PY = 10.c) Using these individual demand curves, construct the market demand curvefor total X. What is the algebraic equation for this curve?2d) Now suppose I1 increases to 1100 and I2 decreases to 900. How would themarket demand curve shift? How would the individual demand curves shift?Graph these new curves.e) Suppose PY rises to 15. Graph the new individual and market demandcurves that would result.