economy, discuss the concept of pareto optimality = Given, Q-100 Ks La,C Ksh1200, 40, w=30. Determine the quantity of labour and capital that the firm should use in order to maximize output. What is the level of output? (10mks) 110

Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.

100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.

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Firm ABC has estimated that it has the following production function: Q = 1.5LK – 0.3L2 – 0.15K2 Labor (L) has a price of €60 and capital (K) has a price of €75. ABC wants to maximize the production with a total cost of €2025. (a) Determine the quantities of labor and capital the firm should use. (round results to 2 decimal places) (b) What quantity of output will be produced at the optimal combination of factors of production?

Q(K, L) = 4K²L2 Type your answers in all of the blanks and submit The production function of good x is as follow: a. What is the marginal production of capital with 16 labor and 4 capital? Type your answer her b. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 10 labors and 400 units of capital. Slope = Type your answer her (absolute value.) c. If we increase the amount of labor we use in our production process from 10 to 1000 units, how much change in capital is needed for us to stay on the same isoquant? Change in K= Type your answer here (Actual value, negative if decrease and positive if increase) d. Is diminishing return a characteristic of this production function? For labor? (yes/no) Type your answer her ;For Capital (yes/no)? Type your answer here

oboard S Font Paragraph S Sensitivity Styles Editing Voice A Cobb-Douglas production function for new company is given by FF(KK, LL) = KK3/5LL2/5 where K represents the units of capital and L represents the units of labor. Suppose units of labor and capital cost $200 and $100 each respectively. If the budget constraint is $30,000, find the maximum production level for this company. VAAAWMMAA AAAAAAAAA SAAAAAAA

Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.

Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale

According to the law of diminishing returns, if a factory keeps adding more workers while keeping the amount of machinery constant, eventually: 0000 Total output will start to decrease. Output per worker will start to increase. The additional output generated by adding another worker will start to decrease. The factory will become more efficient.