Question: Ming has income m and the utility function u(x1, x2) = 8x1 - (x1)+ x2 where and 2 are the quantities of the two

Ming has income m and the utility function u(x1, x2) = 8x1 

Ming has income m and the utility function u(x1, x2) = 8x1 - (x1)+ x2 where and 2 are the quantities of the two goods consumed. The price of good 1 is p and the price of good 2 is p2 = 1. (a) Find Ming's demand functions for goods 1 and 2 for any p> 0 and m> 0 [be careful about potential corner solution]. (b) Suppose initially p = $2 and m = 30. Find Ming's optimal consumption bundle. (c) Now suppose p increases from $2 to $4, while still m = 30 and p2 = 1. Find the income and substitution effects of this price change on the quantity demanded for each good. Is good 1 ordinary? Is good 1 normal? Explain. Now suppose there are 20 consumers identical to Ming in the market for good 1. (d) Find the market demand function, q (p) for good 1 for any p > 0. Is market demand elastic at p = 2? (e) Find the inverse market demand function for good 1 and plot the demand curve. (f) At what price and quantity of good 1 is total revenue q (p)p maximized? What is the value of marginal revenue at that price and quantity? Explain why.

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