A firm uses two inputs to produce a single product. If its production function is Q = x¹/4y¹/4 and if it sells its output for a dollar a unit and buys each input for $4 dollars a unit, find its profit-maximizing input bundle. (Check the second order conditions.)
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- A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the firm’s production possibility set, and its input requirement set. 2. Is this production function concave, quasi-concave? 3. Is this production function homogenous? 4. Find its returns to scale when X1=1, and X2=1A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?From the table attached below, which plant will the firm choose for producing 18 chocolates per day if each worker costs $15 per day and each machine costs $50
- A shoe factory has 500 employees and produces a thousand pairs of shoes per hour. What is the shoe factory’s productivity per worker per hour?____________. The factory hires one new worker. Now, the factory produces 1,002 shoes per hour. Then the factory hires one more worker. Production rises to 1,004 per hour. Does the factory have diminishing, constant, or increasing marginal returns at this level of production? Graph the production function (total product curve) of the shoe factory at these levels of production, carefully labeling all lines and points. (need a clear and properly labelled diagram please)Suppose that the production function is given by y = 2x0.5 The price of x is $3 and the price of y is $4. Derive the corresponding VMP and AVP functions. What is MFC? Solve for the profit-maximizing level for input use x.Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
- Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price of labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes.Is this graph a valid set of cost curves? True/FalseQ1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two markets
- Consider a beekeeper. The beekeeper has the following production function where the input is the number of hives and the output is quantity of honey produced. Beehives 1 2 3 4 5 6 7 8 9 10 11 Honey 12 23 33 42 50 57 66 71 75 78 80 The cost of installing a beehive is $100 and the price of a unit of honey (whatever that is...) is $20. Also each beehive increases the output of apples at a nearby apple orchard by $40. QUESTION 1,2,3 have already been answer I only need the explaination and answer for question 4 and 5 1. What is the efficient number of beehives? 2. If there are barriers to negotiation between the beekeeper and the orchardist, how many will the beekeeper install? 3. What if the same…A farmer uses K units of machinery and L hours of labor to produce C tons of corn, with the production function, C = 2 L0.5 K. The farmer currently uses L = 20 and K = 10. Suppose the input price ratio is w/r = 1. What would you tell the farmer to do in order to minimize his cost of production given the current level of output?A firm analyzes the effects of raising its current level of output and finds that doing so will cause its average total cost to increase. If the firm pays both fixed and variable costs of production, which of the following must be true? (Check all that apply) A. The effect of average variable cost increasing dominates the effect of average fixed cost decreasing B. The marginal cost is greater than the average total cost C. The marginal cost curve is less than the average total cost D. The effect of average fixed cost decreasing dominates the effect of average variable cost increasing
