ECONOMICS:PRIN.+POLICY-MINDTAP (1 TERM)
14th Edition
ISBN: 9781337912396
Author: Baumol
Publisher: CENGAGE L
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Chapter 8, Problem 4TY
To determine
The profit refused by the firm.
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2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
Chapter 8 Solutions
ECONOMICS:PRIN.+POLICY-MINDTAP (1 TERM)
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- 3. Consider the following three (fictional) data points:Country Ultima Thule Narnia NeverlandGDP per capita (US $, 2021, in thousands) 10 30 20Deaths from COVID-19 as of Jan. 2023, millions 0.24 0.16 0.05(a) What is the slope of the line of best fit through these three points, whereDeaths from COVID-19 is the dependent variable and GDP per capita is theexplanatory variable? (b) The standard error for the slope parameter is 0.009. What does this standarderror measure? (c) Is the slope parameter statistically significant at the 5% level of significance?(The relevant critical value is not the usual value, but 4.303, due to the tinysample size). Explain what this means. (d) Why might this slope parameter be a misleading indicator of the relationshipbetween these two variables?arrow_forwardConsider the following estimated regression equation, where both Rent and Earnings aremeasured in pounds (£) at the individual level (standard errors in parentheses):log(\Rent) = 6.9(0.69)+ 0.9(0.3)log(Earnings),(a) Interpret the coefficient on log(Earnings). (b) If we divided Earnings by 1000, so that it is measured in 1000s of pounds instead of pounds,how would (i) the slope, (ii) the intercept change in the above equation? Now suppose the variable London is added, which is equal to one if an individual iives inLondon, and zero otherwise. The estimated regression equation changes to:log(\Rent) = 6.22(0.622)+ 0.5(0.05)log(Earnings) + 2(0.5)London,(c) Interpret the coefficient on London. (d) Explain why the coefficient on log(Earnings) when London is included in the regression andthe coefficient on log(Earnings) when London is not included in the regression are not thesame.arrow_forward3. Consider the following regression equation, where Cigs is daily spending on cigarettes in poundssterling (£), Y earsEduc is years of education, and F emale equals one if an individual is femaleand zero otherwise (standard errors in parentheses):Cigs [ = 4(1.6)− 0.08(0.032)Y earsEduc − 0.5(0.2)F emale,(a) Interpret the coefficients on Y earsEduc and F emale. (b) What does the model predict the average daily spending on cigarettes would be for womenwith 12 years of education? (c) Form the 95% confidence interval for the coefficient on F emale. (d) Economists are often interested in estimating production functions of the Cobb-Douglas form(Yiis the ith firm’s output, Liits spending on labour, and Kiits spending on capital):Yi = ALαi Kβi,How might someone estimate α and β from this equation using linear regression?arrow_forward
- 2. The demand and supply functions for two interdependent goods X and Y are givenbyQDX = 7 − 4PX + 2PYQSX = −6 + 4PX − PYQDY = 1 + PX − PYQSY = −4 − PX + 2PY(a) Find the market equilibrium condition for each good. (b) Express the equilibrium conditions in the matrix form Ax = b.(c) Find the inverse of matrix A. (d) Given your result in part (c), calculate the equilibrium prices. (e) What is the equilibrium quantity for goods X and Y ?arrow_forward2. A two-sector macro-economic model satisfies the following structural equations:Y = C + I∗C = aY + bwhere 0 < a < 1 and b > 0 are parameters and I∗ denotes investment.(a) What are the exogenous and endogenous variables in this model? (b) Re-arrange this system of equations to express the endogenous variables in terms of the exogenous variables and parameters. (c) Express this system of equations in the matrix form Ax = b. (d) Show that the inverse of matrix A exists.arrow_forwardThe equilibrium prices P1 and P2 for two goods satisfy the equations:−4P1 + P2 = −132P1 − 5P2 = −7(a) Express this system of equations in the matrix form Ax = b. (b) What is the determinant of matrix A? (c) Find the inverse of matrix A. (d) Using matrix algebra, calculate the equilibrium pricesarrow_forward
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