SOLVE WITHOUT COPPYING PLZ
-The customer at position 3,: on the line is assumed to buy from rm 1 if p1+ty2ss2+t{1-s)\" (a) to buy from rm 2 if .l"1+tl'2 2* P2 + til - s)\" (b) and to toss a fair coin if this is an exact equality. Interpretation. Customers care about both price and about the distance they are from the rm. The interpretation of the t is (distance)2 term is that it is a measure of the inconvenience of a consumer for consuming a product that is sway from the meet desired point. As parameter f. gets larger, the two prcducts get more and more diereotistcd. If t = 0 then the products are perfect substitutes. What happens? 1) 1Will either rm i ever set its price p.- 4: of? Why? [I-Iiut: you should discuss two aspects: deformations sud best responses] 2) Suppose that rm 2 sets price 192. At 1whet price can rm 1 capture the entire market (i.e.. given p2, at 1whet p1 1will all the customers buy from rm 1)? Problem 2 The evolution of the aggregate capital stock, K, , and the aggregate production function follow according to K B (1-a)k, and Y, = K, , where Y, is the aggregate 1+ 8 B output of the economy, and B is the discount factor, and is the saving rate, and 1+ B 1-a is labor share, and a is capital share. Y. Q4: Compute the growth rate of the aggregate output, 1+ g, = 141 Y, Q5: Is the growth rate of the aggregate output an increasing function of the saving rate?Consider the 5olow-5wan model with no population growth and no technological progress. bet aggregate consumption be denoted by C; and aggregate output be denoted by. Over time. aggregate investment in physical capital is nanced by savings where total savings at time t is equal to the savings rate. .5, times aggregate output. Aggregate output is produced through use of physical capital. Kt- and labour. Nt- The aggregate production function, which exhibits constant returns to scale and diminishing marginal products with respect to individual inputs. is given by Y; = PHI}, M) with Ni = N. Let Ct denote consumpon-per-capita. kt denote capital-per- capita. and yt = fg) denote output-per-capita. Assume that a steady state exists in per-capita variables with the steady state capital stock following a function 1:13} with the property that dial 3:. I]. In words, assume that the steady state capital stock is higher when the savings rate is higher. 4i Construct the expression relating consumption-per-capita to output-per-capita land implicitly to the capital-per-capital. By taking the derivative of this expression with respect to the savings rate. show that. in the steady state. increasing the savings rate has two opposing forces on steady state consumption-per-capita. [25 marks} With reference to the opposing forces that you found in your answer for Question #4, explain when and why undersaving or oversaving occurs in the steady state
