If you increase the total amount of labor, the labor constraints curve becomes flatter. true or false

i) Derive the output elasticity of labour in the following alternative production function: Y = c + alnk + ßlnL ii) Suppose B = 0.5 and other factors are fixed, explain the unit change in output due to a percentage change in labour.

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a) For an output level of 40 units, calculate the marginal rate of technical substitution between points A and B. b) Also for an output level of 40 units, calculate the marginal rate of technical substitution between points D and E

The fast food company Schnabb uses labor and capital to produce its product. Holding the production fixed, what is the effect of a lower price of capital on the ratio between the number of workers and the amount of capital used? Explain using isocosts and an isoquant.

For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case? a) A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant. b) A firm requires exactly two full-time workers to operate each piece of machinery in the factory.

The slope of isocost AB is Units of capital C 80 60 A 0 B D 60 80 Units of labor greater than the slope of isocost CD. less than the slope of isocost CD. equal to the slope of isocost CD. indeterminate from this information, as the prices of capital and labor are not given. E 120

Suppose a production function is given by the equation Q = LVK. 1. Graph the isoquants corresponding to Q = 10, and Q = 20. 2. MP = √K and MP = 0.5(L/VK). Find the Marginal Rate of Technical Substitution LK (MRTSLK). Do these isoquants exhibit diminishing marginal rates of technical substitution? (Does the slope get flatter as L increases?) 3. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1500 iso-cost curve?

Suppose that when neither input exceeds four times the other, capital and labor are perfect substitutes at a one-to-one ratio. However, once the input ratio reaches four to one in favor of either input, no further substitution is possible. Draw the isoquants.

Tim is a baker who produces doughnuts. He can access labour at a rate of $2 per hour, and capital at a rate of $0.25 per machine hour. He produces doughnuts according to Q = L+ K0.5. If the bakery is operating with an optimal factor allocation, and producing 40 doughnuts per day, determine the average total cost of a doughnut. The bakery employs one worker, Anil, who consumes doughnuts (d) and other goods (y) with utility U(d,y) = edy. (Assume y is the Marshallian good, with Py=$1). %3D Sketch Anil's utility curve, and his budget, which is the pay he receives from his job. Do Anil's preferences satisfy the rules of preference ordering? Are there any constraints on his consumption of either good? Derive the supply and demand curves based on Anil's individual demand, and Tim's costs of production.