Please answer thoroughly and show all steps. Use a simple method if possible and explain.

3. An economy has the perworker production function y 2 3E\1. Assume that prices are flexible and markets clear in the economy with production function Y = F(K, L) = K1/2Ll/2, where K is capital and L labor used in production. (a) Is the production decreasing, constant or increasing return to scale? What are the conditions for the economy to maximize profit? (b) Derive the inflation rate from the quantity theory of money (quantity equation). (c) Suppose money supply increases by 5%, velocity of money circulation increases by 1%, capital increases by 4% and labor increases by 3%, what is the inflation rate? (d) Suppose the real interest rate is 3%, then what is the nominal interest rate for the inflation rate defined in (c). (e) Suppose people are expecting the inflation will go up, but the real income will also go up with real interest rate fixed. How will the price (GDP deflector) fluctuate? 2. Assume that the domestic economy is a small and open with domestic & foreign bonds being perfect substitutes and no restrictions being imposed on international trade in assets. (a) Suppose a party supporting a small government (small public spend- ing and small taxation) won the election and came into power. As- sume also that the new government plans to cut public spending more than the tax and that the marginal propensity to consume is less than one. What is the impact on net export of the new policy by the new government? (b) Suppose a huge foreign country (which is able to influence world in- terest rate) decided to loosen its monetary policy. To deal with this change in world economic environment, the domestic country then set import quota to counter the impact of net export, what are the consequences of these foreign and domestic policies on domestic econ- omy