"With great power comes great responsibility."

- SoPhIsTiCaTeD_fOrD

Review of some basic ideas about the THEORY OF THE FIRM. • How to derive individual and market demand functions • Production isoquants • The marginal rate of technical substitution (MRTS) of labor for capital is MRTSLK = − • MRTSLK = dK = negative of the slope of the isoquant dL M PL M PK

• To move from production function to an isoquant, ﬁx the level of output, Q. Solve for K as a function of L and your ﬁxed Q. Then ﬁnd the derivative of this function. The negative of the derivative is the MRTS. • Deriving long-run cost functions from production function – Recall the cost function is C(Q) = pL L+pK K. The cheapest, best bundle is represented by M PL pL = . M PK pK – Solve for the capital and labor in terms of output, i.e. K = K(pK , pL , Q) and L = L(pL , pK , Q). – Plug these values into the cost function, C = pL L(pL , pK , Q) + pK K(pK , pL , Q) • Deriving short-run cost functions from production function when labor varies but capital is ﬁxed: – Solve for L = L(pL , pK , K, Q) using the given production function. – Plug into cost function: C(Q) = pL L(pL , pK , K, Q) + pK K • Cobb-Douglas production functions: Q = F (L, K) = dLa K b • Constant, increasing and decreasing returns to scale. • Graph of marginal and average functions – If x > 0, marginal function < average function, when average is falling. – If x > 0, marginal function > average function, when average is rising. – The marginal function = average function, when the average function is neither falling nor rising [at a maximum or minimum] 1 d, a, b > 0

1

Short-Run Supply Curve

Assume that ﬁrms are perfectly competitive price takers. This is a reasonable assumption if there are a large number of competing ﬁrms, buyers and sellers know the price everyone is charging and one can eﬀortlessly ﬁnd a ﬁrm charging a lower price. proﬁt = total revenue − total cost π(Q) = P · Q − C(Q) where total cost is equal to variable cost and ﬁxed cost, i.e. C(Q) = V (Q) + F C.1

1.1

Three Important...

• To move from production function to an isoquant, ﬁx the level of output, Q. Solve for K as a function of L and your ﬁxed Q. Then ﬁnd the derivative of this function. The negative of the derivative is the MRTS. • Deriving long-run cost functions from production function – Recall the cost function is C(Q) = pL L+pK K. The cheapest, best bundle is represented by M PL pL = . M PK pK – Solve for the capital and labor in terms of output, i.e. K = K(pK , pL , Q) and L = L(pL , pK , Q). – Plug these values into the cost function, C = pL L(pL , pK , Q) + pK K(pK , pL , Q) • Deriving short-run cost functions from production function when labor varies but capital is ﬁxed: – Solve for L = L(pL , pK , K, Q) using the given production function. – Plug into cost function: C(Q) = pL L(pL , pK , K, Q) + pK K • Cobb-Douglas production functions: Q = F (L, K) = dLa K b • Constant, increasing and decreasing returns to scale. • Graph of marginal and average functions – If x > 0, marginal function < average function, when average is falling. – If x > 0, marginal function > average function, when average is rising. – The marginal function = average function, when the average function is neither falling nor rising [at a maximum or minimum] 1 d, a, b > 0

1

Short-Run Supply Curve

Assume that ﬁrms are perfectly competitive price takers. This is a reasonable assumption if there are a large number of competing ﬁrms, buyers and sellers know the price everyone is charging and one can eﬀortlessly ﬁnd a ﬁrm charging a lower price. proﬁt = total revenue − total cost π(Q) = P · Q − C(Q) where total cost is equal to variable cost and ﬁxed cost, i.e. C(Q) = V (Q) + F C.1

1.1

Three Important...

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