Consider a two-sectors (1, 2), two-inputs (L, K), production side of general equilibrium economy, with variable coefficients production technologies such that sector 1 is capital intensive and sector 2 is labor intensive at all input prices. Use equations and diagrams to derive and compare the Rybczynski lines for labor (L) and capital.
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- In the context of the Heckscher-Ohlin model with the two production factors capital andlabor, we have discussed that industries differ in their labor and capital-intensities.(a) Define labor and capital-intensity of an industry.(b) Explain what we mean when we assume that there are no factor intensity reversals.Illustrate the case of a factor intensity reversal using a suitable diagram.(c) Human activity, particularly the production and consumption of energy-intensive goods and the associated emissions of carbon dioxide into the atmosphere, is a major factor driving global warming. Therefore, the European Union will introduce a carbon border adjustment mechanism (CBAM) in the near future. Imagine a variant of the Heckscher-Ohlin model with two production factors labor and energy used in two industries. Define labor and energy intensity of industry in such a model. Can you think of examples of an energy-intensive industry versus a labor-intensive industry?Explain with the help of Graphs of Total Product (TP) and Marginal product (MP) the three laws of variable proportions and their significance in Industry and agriculture. Give the relationship between TP and MP at different stages of variable proportions. What is the relationship between Average Product curve (AP) and marginal product curve (MP) and explain at what point a progressive firm should change its labor or capital inputs with more skilled labor or with new technological machine in order to remain comparative in the market. What would happen to its product in the market if it does not change its machines or if it changes all its machines at the same time157.In an economy with flexible prices, competitive factor markets, and fixed supplies of the factors of production, graphically illustrate the impact of a deadly virus that kills a large part of the labor force, but leaves the other factors of production untouched, ceteris paribus. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; and v. the terminal equilibrium values. Explain in words how the equilibrium values change. 158.Assume that the production function is given by Y = AK0.5L0.5, where Y is GDP, K is capital stock, and L is labor. The parameter A is equal to 10. Assume also that capital is 100, labor is 400, and both capital and labor are paid for their marginal products. a.What is Y? b.What is the real wage of labor? c.What is the real rental price of capital (the amount of output paid per unit of capital)? 159.Assume that GDP (Y) is 6,000. Consumption (C). is given by the equation C = 600 + 0.6(Y…
- explain your anwer with clearly and fully labeled graphs. The change in the optimal capital-labor ration if both inputs are perfect complements inproduction and both their prices increase by an identical percentage. Assume the totalcost before and after the change in input prices remains the same.Figure 2 represents the Texas labor market. In this simplified model, labor and capital are the only factors of production. The initial supply of labor is denoted by S0 and consists entirely of U.S. workers. The demand for labor is denoted by D. Quantity of workers are in thousands and the wage rate is for a 40-hour workweek. (a) At labor market equilibrium, what is total weekly labor income? (b) At labor market equilibrium, what is the weekly income earned by U.S. capital owners? (Note: the capital owners are on the demand side – the demand curve reflects their demand for labor -- so the consumer surplus is the capital owner’s income.) Mexican labor migration yields a new labor supply curve, S1, which is the combination of domestic labor supply and Mexican labor. Given this: (c) What is total weekly labor income?(d) What is the weekly income earned by U.S. capital owners?Consider an economy consisting of traditional cottage industry with perfect competition andincreasing returns to scale manufacturing industry where urban dweller's demand may be moreconcentrated in manufactured goods in which a minimum of workers has to be employed givingrise to a different production functions for both industries. Wage rate may significantly varybetween cottage and manufacturing industry along with identical market price.How does industrialization create market failure so that public policy should initiate toswell the process of economic uplift? Even if there is homogeneity of wage rate betweentraditional cottage and manufacturing industries, Is there any way multiple equilibria may existwhen many product sectors invest at a time. Why or why not?
- (a) Show that the production function Q = (Kα + Lα)β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.(b) Specify a translog cost function for two inputs and show that the input shares depend on inputprices.Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. (a) Write down the definition of a competitive equilibrium for the above economy 1 (b) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, lump-sum tax, T , and output, Y in equilibrium. (c) Solve for the optimal allocation of leisure, l, the consumption, c, employment, N, output, Y . Contrast these quantities with those…Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. Answers for part b below: A consumer's choice of optimizing its consumption and labor hours (h - l ) is given by the point where , MRS(c , l) = wage rate Now , MRS (c, l) = MU(c) /MU(l) MU(c) = dU/d c = a/c MU(l) = dU /dl = (1-a )/l MRS = a (l)1−a (c)a (l)1-a (c) Putting this in optimal condition we have : a (l)(1−a) (c)a (l)(1-a) (c) = w --- (i) l = w…
- Which of the following statements is true? (a) If a firm is experiencing decreasing returns, it will face increasing opportunity costs and hence will have a convex production possibility frontier. (b) If a firm has a steep average total cost curve, then it will have fairly low fixed costs as a proportion of total costs and would incur only a low cost penalty if output declines. (c) A firm with a concave production function at all levels of output would face a convex total cost function at all levels of output. (d) If a firm faces diminishing returns, then at low levels of output, the average variable cost effect would dominate, but at higher levels of output, the average fixed cost effect would dominate.Suppose that wine and cloth are constant returns to scale industries that always use the two inputs (land and labor) in the same proportion. That is, one unit of land must be used in conjunction with one unit of labor to get one unit of output. Assume that the initial endowment is 50 units of land and 60 units of labor. Draw the production possibility frontier between wine and cloth. Be sure to label your picture.A firm that used only labor and capital in production incurs a total cost of ₱4,000.00. The wage rate of labor is 100pesos and a unit of capital cost 200 pesos.b. What is the isocost function of the firm? c. Graph the isocost of the firm by plotting units of capital on the y-axis and units of labor on the x-axis. d. What is the relative price between the two inputs of production? e. If the price of a unit of labor becomes 400 pesos, what is the isocost function of the firm? f. Graph the new isocost line of the firm on the same set of axes in (b).