2.4 Draw the isoquants and find the cost function corresponding to each of the following production functions: Case A : q=2²¹293 Case B : q=a1²1 + a₂%2 Case C : q=a1²² +₂2 Case D : 9 = min { 21 221 01 02 where q is output, z₁ and 22 are inputs, a1 and as are positive constants. [Hint: think about cases D and B first; make good use of the diagrams to help you find minimum cost.] 1. Explain what the returns to scale are in each of the above cases using the production function and then the cost function. (Hint: check the result on page 25 to verify your answers] 2. Discuss the elasticity of substitution and the conditional demand for inputs in each of the above cases.

Q = a,H + a,L +a,H² +a¸L² +a‚HL , where a,>0 2. Q = aH " L, where a, a, y> 0 a) Derive the equation of the relevant Isoquant. b) Find out whether the production function is well behaved.

1. Assume a daily production function for a firm is Q= min(3L, 4K) a, If L = 100 and K = 100 what quantity is produced? Explain why. b. What would be the cost-minimizing labor and capital combination for this firm to produce Q = 1200? (show your work) Labor = Capital = At this level of production from part b (Q-1200), if the wage rate is: w- $30 and the rental rate of capital is: r= $100, what is the total cost of production? (show your calculations) C.

Please indicate which multiple choice awnser is correct for question 1.1)1.2)1.3)Please indicate it correctly as I have had this awnsered with different letters to the awnser I was told   1.1 - A firm trebles its inputs and discovers that its output rises by a factor of four. This is an example of;Select one or more:a. constant returns to scaleb. diminishing returns to a variable factor c. increasing returns to scaled. economies of scale1.2 - Diseconomies of scale are present when.... Select one or more:a. marginalcostsriseb. long run average costs rise as output rises c. totalcostsfallasoutputrisesd. total costs rise as output rises 1.3 - If the demand for a firm’s product is price inelastic, this implies that Select one or more: a. price changes have no impact on quantity demandedb. a fall in price of 3% will lead to a decline in quantity demanded of more than 3%c. a rise in price will raise total expenditure on the goodd. a 5% rise in price will result in a fall in quantity…

Jeff spends all of his money on housing (H) and other stuff (S) and has a diminishing marginal rate of substitution between housing and stuff. Jeff used to live and work in a small town where housing prices were relatively low. His company has decided to transfer him to a large city where housing prices are higher. (For simplicity, assume that all other prices are the same.) Using a diagram, explain to Jeff's company how to find the amount it needs to raise his salary to keep him just as well after the 2. transfer as he was before. Tridor

13. Suppose you have a production technology given by f(x1, x2) = min{2x₁, x2} and you are producing at the point where x₁ = 10 and x₂ = 20. (a) Explain in words what we mean (generally) by the ‘marginal product' of an input in production. (b) For the production technology in this question and the initial point x₁ = 10 and x2 = 20, what is the marginal product of a small increase in input 1? (c) Suppose input 2 increases and you are now at the initial point x₁ = 10 and x2 = 30. Relative to your answer in part (b), does the marginal product of input 1 decrease, increase, or stay constant? Explain briefly.

The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.

How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?

Which of the following production functions exhibits increasing returns to scale in the factors of production K and L? a. y = ĀK0.3 L0.75 b. y = Kª(ĀL)-e,0 < a < 1 c. y = ĀKO.3L0.3 d. y = ĀK/4 + L³/4

Assume a Cobb-Douglas production function of the form: 3 What type of returns to scale does this production function exhibit? In this instance, returns to scale equal This production function exhibits q=10L0.28K0.59 (Enter a numeric response using a real number rounded to two decimal places.) OA. increasing returns to scale. OB. constant returns to scale. OC. initially decreasing but then constant returns to scale. O D. decreasing returns to scale. O E. initially constant but then decreasing returns to scale.