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- 1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…The price of oil is currently over $80 per barrel and has been as high as $90 per barrel after Saudi Arabia and a couple of oter OPEC countries reduced output this year. The demand for oil is expected to increase by 1 million barely per day over the next year according to the International Energy Agency but OPEC+ has been unclear about its intentions of increasing oil supplies. a. If OPEC+ increases its production by million barrels per day, we can unambiguously say that the equilibrium price will fall, and the equilibrium quantity will rise.Find the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!
- Market Equilibrium A retail chain will buy 900 cordless phones if the price is $10 each and 400 if theprice is $60. A wholesaler will supply 700 phonesat $30 each and 1400 at $50 each. Assuming that thesupply and demand functions are linear, find the market equilibrium point and explain what it means.Given the input-output matrix below, find the output matrix if final demand changes to 500 for water, 180 for electric power, and 800 for agriculture. Industry Electric Power Industry: Water Electric Power Agriculture Other Water 200 100 300 400 The output matrix is X= (Round to two decimal places as needed.) 480 120 240 360 Agriculture Final Demand 180 240 120 60 290 140 600A manufacturer knows that: His TR is given by Revenue = 23Q – Q2 /4 His total cost of production is; Cost = 36 + 2Q + 0.1Q2 Where Q is the weekly production in thousands a) Economists define MR as the rate of change of Total revenue. Derive an expression for Marginal Revenue (MR) b) How do you think Economists’ would define ‘Marginal Cost’? Derive an expression for marginal Cost (MC) and at what output will make marginal Revenue equal Marginal cost? c) Find the total profit and the value of Q that maximizes profit
- Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72If a firm has the production function f(k, I) = (2k1/4 + 14)" what is the firm's elasticity of substitution? O a. G = O b. o = O c. o = 1 O d. a = 2 O e. o = 4 114 -/2K Given the input-output matrix below, find the output matrix if final demand changes to 400 for water, 180 for electric power, and 700 for agriculture. Industry: Water Electric Power Agriculture Other Water 120 120 240 720 The output matrix is X = (Round to two decimal places as needed.) Industry Electric Power 400 200 100 300 8 Agriculture Final Demand 180 240 120 60 260 170 500
- Given the input-output matrix below, find the output matrix if final demand changes to 600 for water, 180 for electric power, and 700 for agriculture. Industry Electric Power Water 120 Agriculture Final Demand 240 320 160 Water 480 270 Electric Power Agriculture Other Industry: 60 120 170 400 180 240 240 360 80 The output matrix is X=. (Round to two decimal places as needed.)Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits. .13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³K+zł Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.