John’s car has an average of 40 miles per gallon (mpg) when using gas from allen’s station and an average of 50 mpg when using gas from bob’s station. john’s preferences are such that he only wants to drive as far as possible given his budget. the gas price is pa dollars at allen’s station and pb dollars at bob’s station. john has a total income of i. write down a utility function u(a, b) that represents john's preferences for gal lons of gas consumed at allen's station, a, and gallons of gas consumed at bob's station b. (hint: treat a and b as two standard consumption goods and find the utility that describes john's preferences for those goods.)

Which of the following pairs is most similar to each other?

The winston company estimates that the factory overhead for the following year will be $1,250,000. the company has decided that the basis for applying factory overhead should be machine hours, which is estimated to be 50,000 hours. the total machine hours for the year were 54,300. the actual factory overhead for the year were $1,375,000. determine the over- or underapplied amount for the year.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a.what is the firm’s labor demand function? b.if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c.now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]