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(C) If shovels rent for $5, and workers must be paid $25, draw several isocost lines. (D) If BBQ-Yee32l has received a state contract to ll 30 potholes, what is the minimum cost at which it can fulll the contract? (E) If the cost of renting a shovel suddenly rises from $5 to $6, what will happen to the composition of inputs that BBQ-Yee321 uses to ll potholes? Why? Aside from catering for outdoor parties, BBQ-Yee32l also x potholes in Bloomington. BBQ-Yee32l's road crews ll potholes using workers and shovels in 1 to 1 correspondence. A worker with 1 shovel can ll 10 potholes in a day. A worker with 2 shovels can still only ll 10 potholes, as can 2 workers with 1 shovel. (A) Draw the production isoquant corresponding to lling 30 potholes. (B) Assume that production displays constant returns to scale, and draw a few more iso- quants. Exercise 6: Vertical Differentiation Suppose a market featuring two goods that differ in quality. Good 1 is of quality s, and good 2 is of quality $2, with $2 > $1. There is a mass of n = 1 consumers, of different types, identified by a taste parameter 0 ~ Ujaj. Consumer's utility function is given by u(0) = 0s' - p if it buys one unit of good with quality s 0 otherwise In what follows, assume s = 1 and s2 = 2. In other words, firms cannot choose their quality, this is given and does not change. Firms cost functions are given by: C(q;) = csiq; for i = 1,2 where q, is the output of firm i. We will also conjecture that parameter values are such that there is full coverage. a) (4 points) Find the taste parameter o that identifies a consumer who is indifferent between buying a unit of good 1 or a unit of good 2. b) (4 points) Derive an expression for the demand functions of each good (i.e., the demand functions that each firm is facing separately). c) (4 points) Set up each firm's problem. Find the firms' reaction functions and solve for the equilibrium prices d) (4 points) Assume now that c = 0.1, a = 1 and b = 3. Find the prices, quantities and profits for each firm. What are the market shares for each firm? Verify that the market is indeed fully covered (Hint: Think on the condition that needs to be met so that the market is fully covered)