Answer Happy

3. (Optional, this question is slightly more advanced than level of this course) Model of Equilibrium Effects Relating to Firm Size and Bribery Example From Lecture Notes: There are two firms, firm A and firm B. Firm A is more productive than Firm B. Both Firms produce a single good, namely y, which is sold for price p. Both Firms face the same Burocracy cost X, while Firm B is 'better connected and so can avoid Burocracy costs by instead paying bribes which cost a fraction b of the Burocracy costs (Firm A is assumed to be unable to pay bribes due to being closely watched by NGOs). Both Firms aim to maximize profits. Total demand in the economy is given if p > Pmax D(p) = { 0 y otherwise (Normally in a general equilibrium model we would want demand to be endogenous, but for simplicity here we make it exogenous.) Firm A has cost function ca(y), and Firm B has cost function cb(y).3 In a world in which no bribery was possible the maximization problem of Firm A is malya PYA – CA(YA) - XYA and the maximization problem of Firm B is тах ув рув — св(ув) – Хув In a world in which bribery is possible the maximization problem of Firm A is maxyA PYA - CA(YA) - XYA and the maximization problem of Firm B is татув рув – св(ув) — bХув We make the following assumptions about the cost functions: . CA(T) <0B(0) Ca(%) +X > Ca(0) + bX CA(ay) + X = (g((1 – a)y) +bX for some a € [0,1]. . (the existence of such an ais actually implied by first two assumptions) Market clearance requires that yA + YB = y. We assume that Social Welfare is the sum of the consumer surplus, the producer surplus, and the 'civil servant surplus'. The 'civil servant surplus' is the sum of Burocracy costs (their wages) and bribes. Let SW =Social Welfare, CS =Consumer Surplus, CSS =Civil Servant Surplus, and PS =Producer surplus; so SW = CS + PS + CSS.
(a) For economy without bribery, show that yA = y and YB = 0. (Hint: solve firms maximization problems assuming each produces more than zero to get a relationship between price and each of the firms marginal cost, compare results to first of the assumptions about the cost functions.) 3 Assumed to be increasing and convex functions. Continuously differentiable. (b) For economy with bribery, show that yA = ay and yb = (1 - a)y. (Hint: as before, but now look at the first and second assumptions about the cost functions.) Consumer Surplus: For economy without bribery, show that CS = (Pmax – (CA(T)+X))ý, while with bribery CS = (Pmax – (CA(ay) + X))ý. Which is larger? (Hint: from the demand function it follows that CS = (Pmaz – p)y.) (d) Producer Surplus: For economy without bribery, show that PS = (CA(7)+X)ý-CA(7) - Xy, while with bribery PS = [(CA(ay)+X)ay-ca(ay) – Xay]+[(CB((1-a)])+bX)(1- aby - cA((1 – a)y) – bX(1 – a)] (Hint: Producer Surplus is the sum of profits of Firm A and profits of Firm B) Civil Servant Surplus: For economy without bribery, show that CSS = Xy, while with bribery CSS = Xay +bX(1 - a)y. (Hint: recall that Civil Servant Surplus is just sum of Burocracy costs and bribes paid) —
(f) Social Welfare: For economy without bribery, show that TS = Pmaxy-CA(5), while with bribery TS = Pmazy – CA(ay) – cb((1 – aby) (g) Conclude that bribery reduces Social Welfare. Discuss who is better off and who is worse off due to existence of bribery (ie. What happens to surpluses of Consumers? Firm A? Firm B? Civil Servants?) (h) Discuss in a few sentences what the model suggests about general equilibrium effects of the kind of micro-level empirical results on bribery that we mentioned in the lecture slides, namely “The (micro-level) evidence about the effect of bribery on economic growth is mixed. Some find it harmful while others believe it helps via a grease the wheels effect. This column argues that the ambiguity can be explained by divergent effects of the mean and dispersion of corruption. A high bribery-mean retards productivity growth of firms, but a high bribery-dispersion facilitates performance of weak firms.” (Source)