exercise 1

Exercises on Budget Constraints and Preferences Exercise 1. (8 points) ii) A consumer has a cash endowment of $20 that they can spend on good X and/or good Y_ These goods are infinitely divisible. On all units of Y. the price of Y is py = $1. On all units of X. the price of X is px = $2 if qx s 5 $1 iqu>5 a) in an X/Y diagram, illustrate the consumer's budget set. In your graph, clearly label the Xwaxis intercept and the Y-axis intercept of the consumer's budget constraint. Is the consumer's budget constraint continuous (i.e. it has no gaps and no jumps)? b) What is the algebraic expression of this budget constraint? ii) Another consumer has a cash endowment of M that they can spend on good X and/or good Y. These goods are infinitely divisible. On all units of Y, the price of Y is by =1. On all units of X. the price of X is px = p if qx S M/Zp 2p if qx > M/2p a) In an X/Y diagram, illustrate the consumer's budget set. In your graph. clearly label the X-axis intercept and the Y-axis intercept of the consumer's budget constraint. b) What is the algebraic expression of this budget constraint