linear utility

Demand curves, linear utility. (15 points) Suppose Teter’s utility function is given by U(X, Y ) = 10X + 4Y , and he has $100 in income. (a) (3 points) Graphically identify the utility maximizing quantities of X and Y if the prices of X and Y are 50 and 10, respectively. Explain why this is the optimal bundle by discussing his willingness to trade off relative to the market. (b) (3 points) Graphically identify the utility maximizing quantities of X and Y if the prices of X and Y are 25 and 10, respectively. Explain why this is the optimal bundle by discussing his willingness to trade off relative to the market. 2 (c) (3 points) Graphically identify the utility maximizing quantities of X and Y if the prices of X and Y are 20 and 10, respectively. Explain why this is the optimal bundle by discussing his willingness to trade off relative to the market. (d) (3 points) Write down the formula for Teter’s demand curve for X when the price of Y is 10 and his income is $100. Note the formula will have multiple pieces. (e) (3 points) Graph Teter’s demand curve for X when the price of Y is 10 and his income is $100.