1. (18 points) Consider an economy where there are consumers of widgets and firms producing widgets. Suppose there are 50 consumers overall within the economy/market. Each consumer has an income of $200 that is used to consumer either widgets or food. Suppose the price of food is P, = $4. Finally, let the utility function for the consumers be: U(q. f) = 4 ln(q) + In (f) where q is the quantity of widgets consumed and f is the food consumed. Suppose that firms are able to easily adjust their production resulting in a long-run cost curve of: C(q) = 50g-8q +0.4q While firms can easily adjust their production, it does take time for this to happen. Initially in the market, suppose there are only 12 firms. (a) (4 points) Find the demand for widgets and food of a single consumer. Reminder: these may be functions since we do not have the price of widgets P (b) (1 point) Given there are 50 consumers, what is the market demand for widgets? (c) (4 points) Use the information about the cost curve to find the supply curve for a single firm. Note: you will need to use the quadratic formula: if az+bx+c=0, - b b - 4ac then z = 2a (d) (1 point) What is the market supply in the short run when there are only 12 firms? (e) (2 points) What is the market Equilibrium in the Short Run? (f) (3 points) Use the cost curve to find the Long Run Supply curve for the market. (g) (3 points) Given the Long Run Supply curve, what would be the Long Run equilibrium in the market? How many firms would be in the market in the long run? Hint: QDQs and QS = firms x 9, LR