y= f(x1,x2)=x1ax2b Derive the equation for an isoquant curve.   If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output.

Suppose isoquant curves are smooth and bend in towards the origin and the cost minimization point is determined by the tangent of the isocost lines and the isoquant. Except all the other options characterize the cost minimization input bundle. (If a condition characterizes the cost minimization input bundle, the condition holds only at the cost minimization input bundle.) O MP /w = MP/r O MRTS = MPL /MPK O MRTS = w/r O MPL/MPK = w/t

After running a successful pineapple business, Diddy looks for a new business venture. Now he wants to run gold mining business named "Diddy Bling Bling" which produces/sells raw gold. For simplicity, two types of inputs are required to produce raw gold (workers and gold mine). In short- run production, the size of gold mine is fixed while the number or workers can vary. After consulting his business consultant, Diddy computes the following cost table. The quantity of raw gold (kilograms) Averaged Total Cost (gold mine size=small) Averaged Total Cost (gold mine size-medium) Averaged Total Cost (gold mine size-Large) 1 700 1400 1800 2 600 1300 1700 3 500 1200 1600 4 400 1100 1500 5 300 1000 1400 6 400 900 1300 7 500 800 1200 8 610 600 1100 9 700 500 1000 10 800 400 900 11 900 375 800 12 1100 250 700 13 1200 400 600 14 1300 490 500 15 1400 600 400 16 1500 700 350 17 1600 800 300 18 1700 900 350 19 1800 1000 400 20 1900 1100 500 21 2000 1200 600 22 2100 1300 700 Draw Diddy Bling Bling's…

The marginal cost of providing a taxi trip is $5.00. Each taxi has the ability to make 20 trips per day. The demand for taxi trips is D(p) = 1,200 - 20p, where demand is the number of rides  per day. Price is measured in dollars. Assume a perfectly competitive industry. How many taxicabs will there be? (Remember, total demand was 1,100 trips.)

A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?   $20 $10 $50 $100

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?

using an isoquant/isocost diagram explain the difference between diminishing returns to a variable factor and decreasing returns to a scale

A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.

Suppose a firm could produce data storage services using two inputs: high capacity hard drive (200 TB) or low capacity hard drive (100 TB).   What is the production function and what is a typical set of isoquant?