A consumer's consumption-utility function for a two period horizon is 0.5 U(cg.G) =c,G" ne consumer's earned income stream is given by mo, mi and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1*. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period Co* and c¡*.

A consumer's consumption-utility function for a two period horizon is 0.5 U(cg.G) =c,G" ne consumer's earned income stream is given by mo, mi and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period Co and c¡*.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.3P

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The expression, M = PXX+ PYY is called a budget constraint where M = amount of money available for expenditure; PX= price of commodity X; PY= price of commodity Y; PXX= expenditure on commodity X; PYY= expenditure on commodity Y. Use M = PXX+PYY to express Y as a function of X and note that the graph of this function is called a budget line. Algebraically derive: (1) the y-intercept; (2) the x-intercept. State what determines the slope of the budget line. Graph the function for M = 120; PX= 3; PY= 5 andshow what happens to the original budget line if M decreases by 25% with PX, PY constant.