The input-Output coefficent matrix for 2-sector economy is given by: 03 03 A = 0.4 0.6 The final demand for two industries are 90 and 520 units respectively. Find the gross output of each sector. What be the labour requirements for each sector?
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- Derive the per-worker production function for this economy if Y=zK2/3N1/3.1d. Given the Input - Output matrices and the final demands, find the value of total production for each of the industries:From the following production functions 1. Q= a1H + a2L + a3H2 + a4 L2 + a5HL, where ai> 0 2. Q = aH@ Ly, where a, @, y > 0 a. Derive the equation of the relevant isoquant. b. Find out whether the production function is well behaved. c. Examine whether the isoquant is well behaved and therefore represents the behaviour of a rational production. d. Derive equation which describes MRTS of 9ne factor. e. For each equation examine whether the production is homogeneous and if so, what is the degree of homogeneity. Is the equation characterized by IRTS, DRTS or CRTS.
- For a production process, the marginal product of labour is given by the equation: MPL= 12L - 0.4L2. The first 18 items produced can be sold for $100 each, and beyond that production level, the unit selling price is $90. What is the marginal revenue product of labour when labour input is 20? a.6800 b.8000 c.9000 d.7500 e.7200Given the following Q=100k0.5 L0.8 C=12000 W=400=500 Determine the quantity of labour and capital Determine the output levelQ.1.20 An upward-sloping labour supply curve illustrates that ceteris paribus; (a) the quantity of labour supplied and the hours of work per week aredirectly related.(b) the quantity of labour supplied and the price of labour used to produceoutput are inversely related.(c) individuals use higher income to buy back leisure time.(d) a greater quantity of labour would be supplied at higher wage rates .Q.1.17 Marginal cost is defined by: (a) total cost increases when one more unit is produced.(b) fixed cost increases when one more unit is produced.(c) Total revenue increases when one more unit is produced.(d) average cost increases when one more unit is produced.
- A19 Subject - economics Consider a constant returns-to-scale production function f(k, l). Show that f(k, l) = k ∂f/ ∂k + l ∂f /∂lA firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is: X=-0.2L3 + 18L2 + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A t what weekly output is marginal cost equal to average variable cost? if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?Suppose that labor is the only input used by East West University. The price of a cheakup is BDT 200 and the equilibrium wage of dentist (labor) is BDT 1000. The table below shows the dentists total product schedule. Quantity of dentists -------------- Quantity of chekups 0 0 2 20 6 40 16 70 a) Draw a table to present the marginal product of labor (MPL) for each dentist and the value of the marginal product of labor (vMPL) per dentist. b) How many dentist should be hired to maximize profit and how many chekups can be produced?
- 6. A company uses two inputs, unskilled labour (L) and capital (K), to produce itsproduct. The wage rate for a unit of labour is €5, while a unit of capital cost €20.a) Determine the equation and plot the isocost line for the company's expenditures on itsinputs of €1,000. Label the intercepts of the isocost with both axes. Draw a typical isoquantfor an output level Q0 and indicate the optimal input levels of L and K. (Do not forget tolabel the axes).b) Suppose the government introduces a minimum wage for unskilled labour of €6 per unit.Show graphically and explain shortly how much it would cost the firm in the short run,with capital input fixed at K, to keep its output constant at Q0.c) Show graphically and comment shortly on the optimal factor mix that the firm would useto produce Q0 in the long run at the specified minimum wage of €6 per unitFrom the table below, what can you infer is the market price in dollars of the product? (# of Labor inputworkers) Total product(# of goods) Marginal Product of Labor (MPL) Marginal Revenue Product of Labor (MRPL) 0 0 - - 1 12 12 $24 2 21 9 $18 3 28 7 $14 4 32 4 $8 5 35 3 $6A representative firm which only can survive for one period. It has the following technology: Y = zF(K,where K is the given capital stock (the representative firm owns K but no market value if the firm sells it). NT is labor demand by paying competitive market wage rate w. and z is total factor productivity (TFP). Let's further assume the production fUnction he a continuous concave function. Without loss of generality, let's assume the output good price equals to I.1. Write down the representative firm's profit function and graphically determine or (not both) mathematically prove the profit maximization condition.