Department of Agricultural and Resource EconomicsEnv Econ 1
University of California at BerkeleyPeter Berck
Fall Semester, 1998
introduction to environmental economics and policy
1.Given production function
a.To draw the isoquant for Q = 3, plot such combinations of K and N, which satisfy
Here are some values of K and N:
b.QN(Q)K(Q)C(Q)
10.524
2148
31.5612
c.Isoquants plot the various combinations of inputs that can be used to produce a given level of output. The slope of an isoquant shows the possibility of substituting one input for another in the production function.
Isoquants farther away from the origin record higher quantities of production. Expenditure lines in the same space represent various combinations of input bundles that cost the same. Expenditure lines closer to the origin represent lower cost bundles of input.
The point at which an expenditure line is tangential to a given isoquant determines the lowest cost bundle of inputs that produces the quantity of output corresponding to the given isoquant.
d.If the price of N decreases to $2 per unit from $4 per unit, the slope of the expenditure line will change: It will become 2/1 from 4/1. Therefore, the point of tangency will shift downward so that the optimal bundle will have more of N and less of K than before the price change.
2.A monopoly occurs when there is some barrier to entry that prevents other firms from entering the market.
Possible entry barriers include:
a.Patents granted by the government that give inventors exclusive rights to sell a new product for a prescribed length of time. This is a legal barrier.
b.Another legal barrier is when a government grants exclusive franchise to a firm to serve a market, such as in the case of public utilities, the post office, etc.
c.A form of technical barrier to entry that leads to monopolies is when the production function exhibits decreasing marginal (and average) costs over a wide range of output levels. These are called natural monopolies.
3.The demand curve that a monopolist faces is the entire market demand. Since the market demand curve is usually downward sloping, the monopolistÕs demand curve is downward sloping. This implies that a monopolist could raise his prices and still continue to sell albeit a lower quantity.
In contrast, a firm in a competitive market is a price taker. Therefore, the demand curve appears to be a horizontal line at the market price. If the competitive firm raises its price, the demand for its goods will drop to zero.
4a.
Êb.
PriceOutput
$/unitQuantityTotal costTRMRMCProfit
852040ÑÑ20
7621422121
6722420120
582340-2117
492436-4112
3103030-660
Êc.From the table above, the quantity at which profit is maximized is 6 for a price of $7 per unit.
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