We have MR'( y)В = 10 and MC'( y)В = 0, so the condition MC'( y) MR'( y) is satisfied.How much does the monopolist produce (as a function of FВ )? What is the price? What is the monopolist's profit? It faces the demand function pВ = 300 5 y. Thus there are two outputs at which MR is equal to MC: 50 and 100/6. Find its output, the associated price, and its profit. It faces the inverse demand function P( y)В =Д¤ 4 y/100. (A more complicated example to show the possibility of two outputs at which MR is equal to MC.)ДЄ monopolist's cost function is TC( y)В = ( y/2500)( y 100) 2В + y, so that MC( y)В = 3 y 2/2500 4 y/25В + 5. The price is 1000 and the monopolist's profit is 10000. Since this profit is positive, the optimal output for the monopolist is the output we have found, namely y*В = 20. The price associated with yВ = 20 is pВ = 1200 (10)(20)В = 1000, so the firm's profit is.Thus any output at which MR is equal to MC satisfies What output maximizes its profit? What is the profit-maximizing price? What is its maximal profit? (Most probably there is at most one output that satisfies the three conditions.) If there is no output that satisfies the three conditions the the optimal output for the monopolist is 0.ДЄ monopolist has the cost function TC( y)В = 200 yВ + 15 y 2 and faces the demand function given by pВ = 1200 10 y. If there are any outputs satisfing these three conditions, the one that has the highest profit is the optimal output for the monopolist.For each output that satisfies the first two conditions, check to see if profit is nonnegative.For each output you find, check to see whether the condition MC'( y*) MR'( y*) is satisfied.Find the output(s) for which MC( y*)В = MR( y*).GOV.UK also has a number of physical activity infographics.Examples and exercises on a profit-maximizing monopolist that sets a single price Examples and exercises on a profit-maximizing monopolist that sets a single price Procedure Physical activity recommendation for other age groups: Physical activity ideas for under 5sДЄll movement counts. To achieve and maintain a healthy weight, they may need to do additional activity and make dietary changes. Watching TV, travelling by car, bus or train, or being strapped into a buggy for long periods are not good for a child's health and development.ДЄll children under 5 who are overweight can improve their health by meeting the activity guidelines, even if their weight does not change. The 180 minutes should include at least 60 minutes of moderate-to-vigorous intensity physical activity.Д¬hildren under 5 should not be inactive for long periods, except when they're asleep. Pre-schoolers should spend at least 180 minutes (3 hours) a day doing a variety of physical activities spread throughout the day, including active and outdoor play. The 180 minutes can include light activity such as standing up, moving around, rolling and playing, as well as more energetic activity like skipping, hopping, running and jumping.ДЄctive play, such as using a climbing frame, riding a bike, playing in water, chasing games and ball games, is the best way for this age group to get moving. This should be spread throughout the day, including playing outdoors. Toddlers should be physically active every day for at least 180 minutes (3 hours). Once babies can move around, encourage them to be as active as possible in a safe and supervised play environment.ДЇor more ideas, see Keeping kids active. Try to include at least 30 minutes of tummy time spread throughout the day when they're awake. If they're not yet crawling, encourage them to be physically active by reaching and grasping, pulling and pushing, moving their head, body and limbs during daily routines, and during supervised floor play. Babies (under 1 year)Д«abies should be encouraged to be active throughout the day, every day in a variety of ways, including crawling. Being physically active every day is important for the healthy growth and development of babies, toddlers and preschoolers.ДЇor this age group, activity of any intensity should be encouraged, including light activity and more energetic physical activity.

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