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- COURSE: MICROECONOMICS - PRODUCTION THEORY Suppose a company engaged in manufacture of wheat whose production function is represented by: Q =10KL.In addition, firm must pay wages of $200 and rent on capital is $600. It is known that firm has a budget of $30,000 for cheese production.a) Calculate break-even point of both factors of production and graph itb) What will happen if minimum wage is now fixed at $300? Graph itc) Assuming that new minimum wage at point b) is maintained and, assuming that investor demands a capital rent of $900, explain what happens to optimal factor level. Graph it1) a) Solve the following inequalities:(i) 5(11 − ?) < ? + 49 (ii) 7? − 3 <10m + 23< 8 − 5m (iii) ?2 ≥ 15 − 2? b) The cost structure for iPhones are as follows, fixed cost of $25 and variable cost perunit of $2. The associated demand function isp = 20 − q .(i) Obtain an expression for the profit, π(q). (ii) Find the range of output which gives a profit of at least $31. c) Use Microsoft Word or Excel to solve the system of linear inequalities:r + 5t ≤ 57t – 2r ≤ 4 r ≥ 0(NB: clearly identify the solution set by placing a BIG enough ‘S’ to coverthat entire region).Crawford Computing finds that its weekly profit, in dollars, from its production and sale of x laptop computers is P(x)=-.002x^3-.15x^2+400x-800 Currently, Crawford builds and sells 9 laptops weekly. (a) what is the current weekly profit? (b) how much profit would be lost if production and sales dropped to 8 laptops weekly? (c) what is the marginal profit with x=9? (d) use answers from parts (a) and (c) to estimate the profit resulting from the production and sale of 10 laptops weekly.
- Suppose that over the short run (say the next 5 years), demand for OPEC oil is given by P = 165 – 2.5q. Here q is measured in millions of barrels a day. OPEC marginal cost per barrel is $15. What is OPEC’s optimal level of production? What is the prevailing price of oil at that level? Many experts contend that maximizing short-run profit is counterproductive for OPEC in the long run because high price reduces buyers to conserve energy and spur competition and new exploration that increases the overall supply of oil. Suppose that the demand curve just described will remain unchanged only if oil prices stabilize at $65 per barrel or below. If oil price exceeds this threshold, long run demand (over a second five year-period) will be curtailed to P = 135 – 2.5q. OPEC seeks to maximize its total profit over the next decade. What is the optimum output and price policy? (assume all values are present values)4. Determine the average function and the marginal function for each of the following functions Totals: a) Total income TR = 100 Q - Q2 b) Total cost TC = 1000+ 10 Q + .01 Q2 c) Total profit TP = 50 Q - 0.1 Q2 - 10003. A firm faces a demand curve given by the function: Q = 100 – 2P Marginal and average costs for the firm are constant at KShs.10 per unit. a) What output level should the firm produce to maximize profits and what are the profits at this output level? b) What output level should the firm produce to maximize revenue and what are the profits at this revenue maximizing output level c) Suppose the firm wishes to maximize revenues subject to the constraint that it earns KShs.12 in profits for each of the 64 machines it employs, what level of output should it produce?
- Question You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=160015) If the average cost (AC) of producing a good is increasing as a firm produces moreoutput (q), then which of the following must be TRUE?A) AFC is falling; AVC is rising; MC > AVCB) AFC is falling; AVC is falling; MC > AVCC) AFC is rising; AVC is rising; MC > AVCD) AFC is rising; AVC is rising; MC < AVCE) AFC is falling; AVC is falling; MC < AVCSuppose a firm is operating in a competitive market and is maximizing profit by producing at thepoint where marginal revenue 5 marginal cost.Now suppose that consumer wealth decreasesin this market (and the good is a normal good).What might you expect to happen to the profitmaximizing output quantity for the firm?
- 10. Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether itproduces any output.a. How does this tax affect the firm’s fixed, marginal, and average costs?b. Now suppose the firm is charged a tax that is proportional to the number of items itproduces. Again, how does this tax affect the firm’s fixed, marginal, and average costs?Give atleast short definition about the statement of the problem given below.You are given the profit function: Profit = 100Q – Q2 – 100 – 0.5Q2a. In words, how would you find the quantity you should produce to maximize profits?b. What is the slope of this line at that optimal profit point, and how does its value tell you that you areat the optimal quantity?c. In words, what would the slope of that line be if you produced a quantity smaller than the optimalquantity? In words, what would the slope of that line be if you produced a quantity greater than theoptimal quantity?
