Cobb Douglas production function

 

Problem 3 (Cost minimization, Cobb Douglas production function) In Florida, in Spring 2020, Doctors without Borders (MSF) organized a mobile clinic to offer Covidl9 testing services to migrant farm hands. The clinic production function was Q = !L”K where Q is the number of migrant workers tested each day, L is the daily number of people working at the clink, and K is the number of pieces of equipment the clinic uses each day. The clinic’s MPL = si and the clinic’s MPK = !Los. a. Does technology at the MSF mobile testing clinic display diminishing marginal returns to labor and/or capital? Explain, clearly. b. What is the expression of the clinic’s Marginal Rate of Technical Substitution? Are the clinic’s isoquants bowed in towards the origin (convex)? How do you interpret this finding? c. Does technology at the clinic display increasing, constant, or decreasing returns to scale? Clearly explain. MSF had an average daily cost of labor of $200 and an average rental cost of equipment of $100. The clinic tested 125 workers each day. d. By using the feasibility condition (output target) and the tangency condition (cost minimizing mix) find the combination of labor and equipment that minimized the clinic’s cost of testing 125 migrant workers. (Keep in mind that the cube root of 125 is 5.) e. What was the clinic’s daily total cost of production? What was the clinic’s unit cost of testing one migrant worker? In a diagram measuring labor (L) along the horizontal axis and equipment (K) along the vertical axis draw an isoquant curve and an iso-cost line to illustrate the clinic’s cost minimizing technique. g. With the aid of your diagram, explain qualitatively how MSF would have changed the combination of workers and pieces of equipment used at the mobile clinic if the rental cost of a piece of equipment increased to $400. In the same Spring, other health organizations set up drive-through testing sites with the same production function as the MSF’s clinic that tested 1,000 people per day. Assume that these health organizations paid the same wages and rental cost of equipment as MSF. h. How many workers were used each day at a drive-through testing site? How many pieces of equipment? i. What was the daily cost of testing at a drive-through testing site? What was the unit cost of testing one person? Why were the drive-through testing sites more efficient than MSF’s mobile clinic?

 

 

Sample Solution

came to power in 1979 and represented for many, laissez-faire economics and individual self-determination (Steele, 2018). She believed in power of the market, utilizing it to restore the stagnant British economy and moving away from state provided services. In 1979, cuts resulted in reducing the standard rate of tax from 33% to 30%, the top rate from 83% to 60% and finally cutting public spending by 3% (Bolick, 1995). She reduced the amount of public spending, from 50% to 43%. Thatcher felt high taxes discouraged the incentive to work however, effects of tax cuts increased income inequality through as high earners saw ‘the top 10%- did far better, with their incomes increasing from the equivalent of £472.98 in 1979 to £694.83 in 1990’. The uneven distribution of wealth saw the poorest families receive the least. Reductions in public expenditure affected health, education and social services which created a knock-on effect with substantial loss of public sector jobs resulting in decreased spending on goods and services. Privatisation became Thatcher’s most important and long-lasting legacy. She revealed in her memoirs that it was crucial for ‘reversing the corrosive and corrupting effects of socialism’ Parker. In the 1980-90s, due to fiscal pressures, Thatcher’s conservative views on private ownership and public discontent with the current regime saw the privatisation of public owned entities. For example, the sale of just ‘over 50% of shares in BT and the sale of British Energy in 1996’ (Berrington, 1998). Other privatised industries included electricity, gas, British steel, public bus transportation and other public services. As a result, workforces declined as ‘employment in the electricity and gas industries was cut in half’(Edwards, 2017), problems arose in the regulation of private monopolies to prevent abuse of power, however improved ‘economic growth and improved living standards as privatised businesses cut costs, increased service quality’ (Edwards, 2017). Thatcher can be seen as the key instigator of the sweeping shift from traditional to ‘New Public Management’ initiated by public service reforms. NPM involved the adoption of private sector management ideas to improve structures and processes in the public sector. Thatcher who led the 1980s ‘New Right’ administrations, that put a ‘shrinking government and reduced taxation on the agenda’ (Ferlie, 2017). Thatcher also wanted to remove ‘inefficiency in the state bureaucracy and the deprivilege of the civil service’ as she concluded that the public sector was ‘wasteful, overbureaucratic and underperforming’ (Ferlie et al., 1996). Thatcher wanted to identify areas of waste and inefficiency in the government and ‘improve service quality and customer-orientated service’ (Pollitt, 1996) whilst reducin

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