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Average Product” as “Average output per employee.” MP has to do with the extra output produced by the last person that was hired. Q (L,K) = a + bL + cL2 +dL3 only labor is in the SR production formula. Q (L,K) = a + bKL + cK2L2 +dK3L3 (Both labor and capital are in LR formula.) TFC =Total Capital Costs = rK Here “r” represents the “capital costs over the specified time period for 1-unit of capital K.” TC = wL + rK, w = wage rate paid to each laborer (per time period),L = number of units of labor used (in that time period),r = capital costs paid for each unit of capital (per time period),K = number of units of capital used (in that time period). Costs = f(Q). Q = f(L). Costs = f(Q(L)). Q=AP*L, MP equals AP, at highest AP. Whereas, MC equals AVC at lowest AVC. when we are at maximum average product (MP = AP), we are also at minimum average variable cost (SMC = AVC). average labor efficiency is at its max, we are producing with the fewest possible laborers, so our average labor costs are at their minimum. production function” expresses the relationship between labor input and the firm’s output (total product). a short-run S-shaped production function (where labor productivity increases at increasing rates in early ranges and then increase at decreasing rates in later ranges) take this form:Q = -aL3 + bL2 . Lmax AP = -B/2A. MP = dQ/dL = 3AL2 + 2BL. MP (the value of the slope) first increases, reaches a max and then decreases. L max MP = -B/3A. Max MP occurs before Max AP. If Q = AL3 + BL2 (A<0, and B>0)Ave roduct = AP = Q/L = AL2 + BL,Marg Product = dQ/dL = 3AL2 + 2BL,The amount of labor units to hire to produce Max Ave Product = -B/2A (= L max AP ),The amount of labor units to hire to produce Max Marg Product = -B/3A (= L max MP ). Total costs first increase at a decreasing rate (at lower levels of labor) due to early productivity gains of labor (economies-of-scale). But total costs ultimately begin to rise at increasing rates as the productivity of labor decreases (diseconomies-of-scale). TC = FC + aQ + bQ2 + cQ3. first AVC decreases, then it increases. min AVC occurs when d(AVC)/dQ = 0. Q = -b/2c. SMC ≡ d(TC)/dQ =d(TVC)/dQ, Q= -b/2c when SMC = AVC that’s min AVC. SMC = AVC that intersection occurs at min AVC (and can be found by finding Q = -b/2c). both AVC and SMC will be “U-shaped.” AP and MP, when marginal product is greater than average product, average product is increasing. SMC>AVC, AVC is increasing. SMC<ATC , ATC is decreasing. As the capital stock increases for each level of labor usage, the marginal product of labor increases, the additional unit of labor is more productive because it has more capital with. First line mc=(tc-fc)/units. When SMC is greater than AV ,AVC is increasing. When SMC is greater than ATC,ATC is increasing. When AP is increasing, AVC is dereasing, when MP is increasing , MC is decreasing. All coefficients are statistically significant at the ** percent level of significance because all p-values are less than **. Competitive firm’s demand is perfectly infinitely elastic at every quantity.MR = P for perfect competitor, P = D = MR, each individual PC-firm faces the same “horizontal demand curve. inverse) demand line. Although each firm faces a horizontal demand curve, the aggregate demand curve (price line) for the industry is downward sloping. π = (P – ATC) * Q. when market price = the company’s min AVC, the PC firm should set Q* to MR = MC (P = SMC) to find 250 units. And at that profit- max output, the price that the PC-firm receives is just = the PC-firm’s TVC. After paying its TVC, the company has nothing left to pay its TFC. As long as the company can pay its TVCs, it should operate. when the company faces a market price that is less than its min AVC, it will not generate enough revenues to cover its TVC. “choose profit maximizing output (Q*) at the point where P = SMC” — we need to amend the rule by saying, “provided that the market price is equal to or...
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