Imagine an economy where a representative state-owned enterprise (SOE) exists alongside a representative private firm. Both firms produce the same good, whose price is normalized to 1. The production functions for the two firms are Yp = Ap Np and Ys = As. Ns, where Np + Ng = N = 1. The private firm has a TFP level that is three times as high as the SOE: Ap = 3 - As. Assume that the private firm and the SOE sell to the same buyers in the same market, and there are no differences between the two firms except for their TFP levels. . Aggregate output is Y = Yp+Ys and aggregate TFP is the same as labor productivity: A = The SOE employs three quarters of the work force (Ns = 3/4). 1. Why might we expect the SOE to have a lower TFP level than the private firm? 2. What is the aggregate TFP level for the economy relative to the level associated with the efficient allocation (i.e. the one which maximizes total output)? Express it in terms of Ap. 3. Suppose the government taxes the private firm's profits at rate 7 and subsidizes the SOE on each unit sold at rate s, so that profits are IIp = (1-7) ApNp - wNp and IIs = (1 +s)As Ns - wNs. Calculate each firm's FOC with respect to labor input. 4. Combine the FOCs above to show that s= 3(1-7)-1. 5. Now suppose the government has a balanced budget: TAPNP Ng = 3/4. = sAs Ns. Solve for the tax and subsidy rates given