1. (18 points) Consider an economy where there are consumers of widgets and rms 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 Pf = $4. Finally, let the utility function for the consumers be: U(q,f) = 41M) +1110\") where q is the quantity of widgets consumed and f is the food consumed. Suppose that rms are able to easily adjust their production resulting in a longrun cost curve of: C(g) = 50g 8q2 + 0.4q3 While rms can easily adjust their production, it does take time for this to happen. Initially in the market, suppose there are only 12 rms. (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 Pm. (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 nd the supply curve for a single rm. N ate: you will need to use the quadratic formula: if (1:132 + 3):): + c = 0, b :I: V b2 4m: then a: = 2a (d) (1 point) What is the market supply in the short run when there are only 12 rms? (2 points) What is the market Equilibrium in the Short Run? (3 points) Use the cost curve to nd the Long Run Supply curve for the market. A O'Q Ham VVV (3 points) Given the Long Run Supply curve7 what would be the Long Run equilibrium in the market? How many rms would be in the market in the long run? Hint: QB = Q5 and Q3 = nms >